Analysis of a tuberculosis model with undetected and lost-sight cases
•A tuberculosis model with undetected infectious and lost-sight cases is analyzed.•The model exhibits the phenomenon of backward bifurcation.•Backward bifurcation occurs only for high and unrealistic ranges of reinfection rates.•For random values of the reinfection rates, the disease dies out. A det...
Saved in:
| Published in | Communications in nonlinear science & numerical simulation Vol. 41; pp. 48 - 63 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.12.2016
Elsevier |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | •A tuberculosis model with undetected infectious and lost-sight cases is analyzed.•The model exhibits the phenomenon of backward bifurcation.•Backward bifurcation occurs only for high and unrealistic ranges of reinfection rates.•For random values of the reinfection rates, the disease dies out.
A deterministic model of tuberculosis (TB) in sub-Saharan Africa including undetected and lost-sight cases is presented and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, when a stable disease-free equilibrium co-exists with one or more stable endemic equilibrium points when the associated basic reproduction number (R0) is less than unity. Analyzing the model obviously reveals that exogenous reinfection plays a key role on the existence of backward bifurcation. However, an analysis of the ranges of exogenous reinfection suggested that backward bifurcation occurs only for very high and unrealistic ranges of the exogenous reinfection rate. Random perturbation of reinfection rates was performed to gain insight into the role of this latter on the stability of the disease free equilibrium. |
|---|---|
| AbstractList | A deterministic model of tuberculosis (TB) in sub-Saharan Africa including undetected and lost-sight cases is presented and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, when a stable disease-free equilibrium co-exists with one or more stable endemic equilibrium points when the associated basic reproduction number (R sub(0)R0) is less than unity. Analyzing the model obviously reveals that exogenous reinfection plays a key role on the existence of backward bifurcation. However, an analysis of the ranges of exogenous reinfection suggested that backward bifurcation occurs only for very high and unrealistic ranges of the exogenous reinfection rate. Random perturbation of reinfection rates was performed to gain insight into the role of this latter on the stability of the disease free equilibrium. •A tuberculosis model with undetected infectious and lost-sight cases is analyzed.•The model exhibits the phenomenon of backward bifurcation.•Backward bifurcation occurs only for high and unrealistic ranges of reinfection rates.•For random values of the reinfection rates, the disease dies out. A deterministic model of tuberculosis (TB) in sub-Saharan Africa including undetected and lost-sight cases is presented and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, when a stable disease-free equilibrium co-exists with one or more stable endemic equilibrium points when the associated basic reproduction number (R0) is less than unity. Analyzing the model obviously reveals that exogenous reinfection plays a key role on the existence of backward bifurcation. However, an analysis of the ranges of exogenous reinfection suggested that backward bifurcation occurs only for very high and unrealistic ranges of the exogenous reinfection rate. Random perturbation of reinfection rates was performed to gain insight into the role of this latter on the stability of the disease free equilibrium. A deterministic model of tuberculosis (TB) in sub-Saharan Africa including undetected and lost-sight cases is presented and analyzed. The model is shown to exhibit the phenomenon of backward bifurca-tion, when a stable disease-free equilibrium co-exists with one or more stable endemic equilibrium points when the associated basic reproduction number (R 0) is less than unity. Analyzing the model obviously reveals that exogenous reinfection plays a key role on the existence of backward bifurcation. However, an analysis of the ranges of exogenous reinfection suggested that backward bifurcation occurs only for very high and unrealistic ranges of the exogeneous reinfection rate. Random perturbation of reinfection rates was performed to gain insight into the role of this latter on the stability of the disease free equilibrium . |
| Author | Bowong, S. Nana Yakam, A. Moualeu, D.P. Temgoua, A. |
| Author_xml | – sequence: 1 givenname: D.P. surname: Moualeu fullname: Moualeu, D.P. organization: Institute for Horticultural Production Systems, Vegetable Systems Modelling Section, Faculty of Natural Sciences, Leibniz Universität Hannover, Herrenhäuser Str. 2, Hannover D-30419, Germany – sequence: 2 givenname: A. surname: Nana Yakam fullname: Nana Yakam, A. organization: Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157, Douala, Cameroon – sequence: 3 givenname: S. surname: Bowong fullname: Bowong, S. email: sbowong@gmail.com organization: Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157, Douala, Cameroon – sequence: 4 givenname: A. surname: Temgoua fullname: Temgoua, A. organization: Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157, Douala, Cameroon |
| BackLink | https://hal.sorbonne-universite.fr/hal-01317636$$DView record in HAL |
| BookMark | eNqNkUtLxDAUhYMo-PwFbrrURWteTduFi0F8wYAbXYfk9tbJ0Em0aUf896aOuBThQm5uvhMu5xyTfR88EnLOaMEoU1frAnz0seDpUlBZUMb3yBGrqzqveCX3U09plZcVlYfkOMY1TWBTyiNyu_Cm_4wuZqHLTDZOFgeY-jBPNqHFPvtw4yqbfIsjwohtZnybpfcxj-51NWZgIsZTctCZPuLZz3lCXu5un28e8uXT_ePNYpmDlPWYA1imhDUVl9JYS1trBTaCNqpUSpSdLC1AU3MwaAVACx3HOpVEwYWRTJyQy92_K9Prt8FtzPCpg3H6YbHU84wywSol1HZmL3bs2xDeJ4yj3rgI2PfGY5iiZjWvGq6Ukv9By1IKLsuEih0KQ4hxwO53DUb1nIVe6-8s9JyFpjKtxJPqeqfCZM7W4aAjOPSArRuSq7oN7k_9F0_-lI0 |
| CitedBy_id | crossref_primary_10_1016_j_health_2022_100111 crossref_primary_10_1186_s12889_020_09260_w crossref_primary_10_1016_j_epidem_2019_100374 crossref_primary_10_3934_mbe_2022509 crossref_primary_10_1007_s12190_023_01984_3 crossref_primary_10_1016_j_amc_2022_126983 crossref_primary_10_1007_s10441_020_09406_8 crossref_primary_10_1016_j_cnsns_2019_104920 crossref_primary_10_1016_j_physa_2019_121274 crossref_primary_10_1080_07362994_2020_1753539 crossref_primary_10_1016_j_chaos_2021_110879 |
| Cites_doi | 10.1016/S0025-5564(02)00108-6 10.1001/jama.282.7.677 10.1007/s11538-005-9057-5 10.1137/S0036139902413829 10.3934/mbe.2004.1.361 10.1006/jtbi.2001.2489 10.1164/rccm.200409-1200OC 10.1126/science.1185449 10.1007/s11538-008-9295-4 10.1038/nri1704 10.1056/NEJM199910143411602 10.1016/j.mbs.2007.01.008 10.1093/imammb/19.2.113 10.1017/S0950268802007148 10.1051/mmnp/20127309 10.1016/S0025-5564(97)00027-8 10.1016/j.mbs.2008.02.005 10.1164/rccm.200606-759OC 10.1007/s002850050069 10.1126/science.273.5274.497 10.1016/j.mbs.2005.12.022 10.1016/S0140-6736(99)01141-1 10.1371/journal.pone.0120607 10.1007/s10852-012-9210-8 10.1137/S0036144500371907 10.1142/S0218339011004159 10.3934/mbe.2004.1.81 10.1016/S0022-5193(03)00038-9 10.1098/rsif.2008.0184 10.1128/JCM.39.6.2213-2218.2001 10.1016/j.jmaa.2004.05.045 10.1016/j.cnsns.2014.06.037 10.1006/tpbi.2000.1451 10.1007/s00285-008-0177-z 10.1186/1471-2334-11-276 10.1016/S0025-5564(00)00003-1 |
| ContentType | Journal Article |
| Copyright | 2016 Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: 2016 – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D 7QL C1K 1XC VOOES |
| DOI | 10.1016/j.cnsns.2016.04.012 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Bacteriology Abstracts (Microbiology B) Environmental Sciences and Pollution Management Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional Bacteriology Abstracts (Microbiology B) Environmental Sciences and Pollution Management |
| DatabaseTitleList | Bacteriology Abstracts (Microbiology B) Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1878-7274 |
| EndPage | 63 |
| ExternalDocumentID | oai_HAL_hal_01317636v1 10_1016_j_cnsns_2016_04_012 S1007570416301149 |
| GroupedDBID | --K --M -01 -0A -0I -0Y -SA -S~ .~1 0R~ 1B1 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VR 5VS 7-5 71M 8P~ 92M 9D9 9DA AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABFNM ABJNI ABMAC ABNEU ABXDB ABYKQ ACAZW ACDAQ ACFVG ACGFS ACNNM ACRLP ADBBV ADEZE ADGUI ADMUD ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AFUIB AGHFR AGUBO AGYEJ AHJVU AIEXJ AIGVJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CAJEA CAJUS CCEZO CCVFK CHBEP CS3 CUBFJ DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FA0 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA HVGLF HZ~ IHE J1W JJJVA JUIAU KOM M41 MHUIS MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q-- Q-0 Q38 R-A R-I R2- RIG ROL RPZ RT1 RT9 S.. SDF SDG SES SEW SPC SPCBC SPD SSQ SST SSW SSZ T5K T8Q T8Y U1F U1G U5A U5I U5K UHS ~G- ~LA AAXDM AAXKI AAYXX AFJKZ AKRWK CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D 7QL C1K 1XC VOOES |
| ID | FETCH-LOGICAL-c448t-ccb163ba7244abb0dbb3e9309656635f45bcc982caeb3ccdcf2e82e84e323a413 |
| IEDL.DBID | AIKHN |
| ISSN | 1007-5704 |
| IngestDate | Tue Oct 15 16:02:10 EDT 2024 Fri Oct 25 22:16:30 EDT 2024 Fri Oct 25 04:48:04 EDT 2024 Thu Sep 26 18:52:35 EDT 2024 Fri Feb 23 02:25:44 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Bifurcation Mathematical models Tuberculosis Stability Nonlinear dynamical systems |
| Language | English |
| License | Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c448t-ccb163ba7244abb0dbb3e9309656635f45bcc982caeb3ccdcf2e82e84e323a413 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| OpenAccessLink | https://hal.sorbonne-universite.fr/hal-01317636 |
| PQID | 1825543245 |
| PQPubID | 23500 |
| PageCount | 16 |
| ParticipantIDs | hal_primary_oai_HAL_hal_01317636v1 proquest_miscellaneous_1827926664 proquest_miscellaneous_1825543245 crossref_primary_10_1016_j_cnsns_2016_04_012 elsevier_sciencedirect_doi_10_1016_j_cnsns_2016_04_012 |
| PublicationCentury | 2000 |
| PublicationDate | December 2016 2016-12-00 20161201 2016-12 |
| PublicationDateYYYYMMDD | 2016-12-01 |
| PublicationDate_xml | – month: 12 year: 2016 text: December 2016 |
| PublicationDecade | 2010 |
| PublicationTitle | Communications in nonlinear science & numerical simulation |
| PublicationYear | 2016 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Verver, Warren, Beyers, Richardson, van der Spuy, Borgdorff (bib0048) 2005; 171 van Rie, Richardson, Victor, Gie, Enarson, Beyers (bib0047) 1999; 341 Elbasha, Gumel (bib0021) 2006; 68 Brauer (bib0012) 2004; 298 Wang (bib0049) 2006; 201 Dye, Williams (bib0020) 2010; 328 Kar, Mondal (bib0029) 2012; 11 Bhunu, Garira, Mukandavire, Zimba (bib0009) 2008; 70 Nunn, Williams, Floyd, Dye, Elzinga, Raviglione (bib0042) 2005; 5 Iggidr, Mbang, Sallet (bib0026) 2007; 209 Bacaër, Ouifki, Pretorius, Wood, Williams (bib0003) 2008; 57 Yang (bib0052) 2002; 19 Kamgang, Sallet (bib0028) 2008; 213 Balabanova, Tchernyshev, Tsigankov, Maximova, Mikheeva, Fedyukovitch (bib0004) 2011; 11 Aparicio, Capurro, Castillo-Chavez (bib0001) 2002; 215 WHO (bib0050) 2012 Hethcote (bib0024) 2000; 42 Feng, Castillo-Chavez, Capurro (bib0022) 2000; 57 Brauer, Castillo-Chavez (bib0013) 2001 Benatar (bib0007) 2006; 15 Iggidr, Kamgang, Sallet, Tewa (bib0025) 2007; 1 Kumar, Abbas, Fausto, Mitchell (bib0031) 2007 Moualeu-Ngangue (bib0036) 2013 van den Driessche, Watmough (bib0046) 2002; 180 Uys, van Helden, Hargrove (bib0045) 2009; 6 Carr (bib0014) 1981 Blower, Small, Hopewell (bib0011) 1996; 273 Castillo-Chavez, Thieme (bib0017) 1995; vol. 1 Murphy, Singer, Kirschner (bib0038) 2003; 223 Dye, Schele, Dolin, Pathania, Raviglione (bib0019) 1999; 282 Moualeu, Mbang, Ndoundam, Bowong (bib0034) 2011; 19 Murray, Styblo, Rouillon (bib0039) 1990; 65 Castillo-Chavez, Song (bib0016) 2004; 1 Wood, Middelkoop, Myer, Grant, Whitelaw (bib0051) 2007; 175 Kribs-Zaleta, Halesco-Hernandez (bib0030) 2000; 164 Begon, Bennett, Bowers, French, Hazel, Turner (bib0006) 2002; 129 Arino, McCluskey, van den Driessche (bib0002) 2003; 64 Hadeler, van den Driessche (bib0023) 1997; 146 Iggidr, Mbang, Sallet, Tewa (bib0027) 2007; 1 Moualeu, Weiser, Ehrig, Deuflhard (bib0035) 2015; 20 NIS (bib0041) 2010 Birkhoff, Rota (bib0010) 1978 Chintu, Mwinga (bib0018) 1999; 353 Moualeu-Ngangue, Röblitz, Ehrig, Deuflhard (bib0037) 2015; 10 Moualeu, Bowong, Emvudu (bib0032) 2011; 29 NCFT. Guide de personnel de la santé. 2001. National Comity of Fight Againts Tuberculosis, Ministère de la Santé Publique du Cameroun. Benatar, Daar, Singer (bib0008) 2005; 2 Castillo-Chavez, Feng (bib0015) 1997; 35 Okuonghae, Korobeinikov (bib0043) 2007; 2 Moualeu, Bowong, Emvudu (bib0033) 2012; 7 Bandera, Gori, Catozzi, Esposti, Marchetti, Molteni (bib0005) 2001; 39 Singer, Kirchner (bib0044) 2004; 1 Feng (10.1016/j.cnsns.2016.04.012_bib0022) 2000; 57 Balabanova (10.1016/j.cnsns.2016.04.012_bib0004) 2011; 11 NIS (10.1016/j.cnsns.2016.04.012_sbref0040) 2010 Moualeu-Ngangue (10.1016/j.cnsns.2016.04.012_bib0037) 2015; 10 Blower (10.1016/j.cnsns.2016.04.012_bib0011) 1996; 273 Dye (10.1016/j.cnsns.2016.04.012_bib0020) 2010; 328 Kar (10.1016/j.cnsns.2016.04.012_bib0029) 2012; 11 Moualeu (10.1016/j.cnsns.2016.04.012_bib0033) 2012; 7 Castillo-Chavez (10.1016/j.cnsns.2016.04.012_bib0015) 1997; 35 WHO (10.1016/j.cnsns.2016.04.012_sbref0049) 2012 Bandera (10.1016/j.cnsns.2016.04.012_bib0005) 2001; 39 Moualeu (10.1016/j.cnsns.2016.04.012_bib0034) 2011; 19 Benatar (10.1016/j.cnsns.2016.04.012_bib0007) 2006; 15 Murray (10.1016/j.cnsns.2016.04.012_bib0039) 1990; 65 Verver (10.1016/j.cnsns.2016.04.012_bib0048) 2005; 171 Arino (10.1016/j.cnsns.2016.04.012_bib0002) 2003; 64 Iggidr (10.1016/j.cnsns.2016.04.012_bib0025) 2007; 1 Benatar (10.1016/j.cnsns.2016.04.012_bib0008) 2005; 2 Moualeu-Ngangue (10.1016/j.cnsns.2016.04.012_bib0036) 2013 Brauer (10.1016/j.cnsns.2016.04.012_bib0012) 2004; 298 Nunn (10.1016/j.cnsns.2016.04.012_bib0042) 2005; 5 Wang (10.1016/j.cnsns.2016.04.012_bib0049) 2006; 201 Murphy (10.1016/j.cnsns.2016.04.012_bib0038) 2003; 223 Castillo-Chavez (10.1016/j.cnsns.2016.04.012_bib0016) 2004; 1 Castillo-Chavez (10.1016/j.cnsns.2016.04.012_bib0017) 1995; vol. 1 Kumar (10.1016/j.cnsns.2016.04.012_sbref0031) 2007 Kamgang (10.1016/j.cnsns.2016.04.012_bib0028) 2008; 213 Birkhoff (10.1016/j.cnsns.2016.04.012_bib0010) 1978 Carr (10.1016/j.cnsns.2016.04.012_bib0014) 1981 van Rie (10.1016/j.cnsns.2016.04.012_bib0047) 1999; 341 Kribs-Zaleta (10.1016/j.cnsns.2016.04.012_bib0030) 2000; 164 Bhunu (10.1016/j.cnsns.2016.04.012_bib0009) 2008; 70 Iggidr (10.1016/j.cnsns.2016.04.012_bib0027) 2007; 1 Hethcote (10.1016/j.cnsns.2016.04.012_bib0024) 2000; 42 van den Driessche (10.1016/j.cnsns.2016.04.012_bib0046) 2002; 180 10.1016/j.cnsns.2016.04.012_bib0040 Aparicio (10.1016/j.cnsns.2016.04.012_bib0001) 2002; 215 Moualeu (10.1016/j.cnsns.2016.04.012_bib0035) 2015; 20 Brauer (10.1016/j.cnsns.2016.04.012_bib0013) 2001 Yang (10.1016/j.cnsns.2016.04.012_bib0052) 2002; 19 Singer (10.1016/j.cnsns.2016.04.012_bib0044) 2004; 1 Okuonghae (10.1016/j.cnsns.2016.04.012_bib0043) 2007; 2 Chintu (10.1016/j.cnsns.2016.04.012_bib0018) 1999; 353 Elbasha (10.1016/j.cnsns.2016.04.012_bib0021) 2006; 68 Hadeler (10.1016/j.cnsns.2016.04.012_bib0023) 1997; 146 Uys (10.1016/j.cnsns.2016.04.012_bib0045) 2009; 6 Dye (10.1016/j.cnsns.2016.04.012_bib0019) 1999; 282 Moualeu (10.1016/j.cnsns.2016.04.012_bib0032) 2011; 29 Begon (10.1016/j.cnsns.2016.04.012_bib0006) 2002; 129 Bacaër (10.1016/j.cnsns.2016.04.012_bib0003) 2008; 57 Iggidr (10.1016/j.cnsns.2016.04.012_bib0026) 2007; 209 Wood (10.1016/j.cnsns.2016.04.012_bib0051) 2007; 175 |
| References_xml | – year: 2013 ident: bib0036 publication-title: A mathematical tuberculosis model in cameroon, [Ph.D. thesis] contributor: fullname: Moualeu-Ngangue – volume: 1 start-page: 506 year: 2007 end-page: 519 ident: bib0027 article-title: Multi-compartment models publication-title: Discret Contin Dyn Syst Ser B contributor: fullname: Tewa – volume: 180 start-page: 28 year: 2002 end-page: 29 ident: bib0046 article-title: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission publication-title: Math Biosci contributor: fullname: Watmough – volume: 19 start-page: 113 year: 2002 end-page: 135 ident: bib0052 article-title: The effects of re-infection in directly transmitted infections modeled with vaccination publication-title: IMA J Math Appl Med Biol contributor: fullname: Yang – volume: 7 start-page: 117 year: 2012 end-page: 146 ident: bib0033 article-title: Analysis of the impact of diabetes on the dynamics transmission of tuberculosis publication-title: Math Model Nat Phenom contributor: fullname: Emvudu – volume: 29 start-page: 1097 year: 2011 end-page: 1116 ident: bib0032 article-title: Global properties of a tuberculosis model with publication-title: JAMI contributor: fullname: Emvudu – volume: 341 start-page: 1174 year: 1999 end-page: 1179 ident: bib0047 article-title: Exogenous reinfection as a cause of recurrent tuberculosis after curative treatment publication-title: N Engl J Med contributor: fullname: Beyers – volume: 19 start-page: 683 year: 2011 end-page: 723 ident: bib0034 article-title: Modeling and analysis of HIV and hepatitis publication-title: J Biol Syst contributor: fullname: Bowong – volume: 5 start-page: 819 year: 2005 end-page: 826 ident: bib0042 article-title: Tuberculosis control in the era of HIV publication-title: Nat Rev Immunol contributor: fullname: Raviglione – volume: 223 start-page: 391 year: 2003 end-page: 404 ident: bib0038 article-title: On the treatment of tuberculosis in hetergeneous populations publication-title: J Theor Biol contributor: fullname: Kirschner – volume: 15 start-page: 322 year: 2006 end-page: 330 ident: bib0007 article-title: Facing ethical challenges in rolling out antiretroviral treatment in resource-poor countries: Comment on “they call it ‘patient selection’ in khayelitsha” publication-title: Camb Q Healthc Eth contributor: fullname: Benatar – year: 2007 ident: bib0031 publication-title: Basic pathology contributor: fullname: Mitchell – volume: 201 start-page: 58 year: 2006 end-page: 71 ident: bib0049 article-title: Backward bifurcation of an epidemic model with treatment publication-title: Math Biosci contributor: fullname: Wang – volume: 1 start-page: 361 year: 2004 end-page: 404 ident: bib0016 article-title: Dynamical models of tuberculosis and their applications publication-title: Math Biosci Eng contributor: fullname: Song – year: 1978 ident: bib0010 publication-title: Ordinary differential equations contributor: fullname: Rota – year: 2012 ident: bib0050 article-title: Global tuberculosis control: Surveillance, planning, financing contributor: fullname: WHO – volume: 57 start-page: 557 year: 2008 end-page: 593 ident: bib0003 article-title: Modeling the joint epidemics of TB and HIV in a South African township publication-title: J Math Biol contributor: fullname: Williams – volume: 353 start-page: 997 year: 1999 end-page: 1005 ident: bib0018 article-title: An African perspective of tuberculosis and HIV/AIDS publication-title: Lancet contributor: fullname: Mwinga – volume: 11 start-page: 433 year: 2012 end-page: 459 ident: bib0029 article-title: Global dynamics of a tuberculosis epidemic model and the influence of backward bifurcation publication-title: J Math Model Algorithm contributor: fullname: Mondal – volume: 171 start-page: 1430 year: 2005 end-page: 1435 ident: bib0048 article-title: Rate of reinfection tuberculosis after successful treatment is higher than rate of new tuberculosis publication-title: Am J Respir Crit Care Med contributor: fullname: Borgdorff – volume: 146 start-page: 15 year: 1997 end-page: 35 ident: bib0023 article-title: Backward bifurcation in epidemic control publication-title: Math Biosci contributor: fullname: van den Driessche – volume: 213 start-page: 1 year: 2008 end-page: 12 ident: bib0028 article-title: Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE) publication-title: Math Biosci contributor: fullname: Sallet – volume: 10 start-page: e0120607 year: 2015 ident: bib0037 article-title: Parameter identification in a tuberculosis model for cameroon publication-title: PloS One contributor: fullname: Deuflhard – volume: 129 start-page: 147 year: 2002 end-page: 153 ident: bib0006 article-title: A clarification of transmission terms in host-microparasite models : Numbers, densities and areas publication-title: Epidemiol Infect contributor: fullname: Turner – volume: 1 start-page: 260 year: 2007 end-page: 278 ident: bib0025 article-title: Global analysis of new malaria intrahost models with a competitive exclusion principle publication-title: SIAM J Appl Math contributor: fullname: Tewa – volume: 6 start-page: 11 year: 2009 end-page: 15 ident: bib0045 article-title: Tuberculosis reinfection rate as a proportion of total infection rate correlates with the logarithm of the incidence rate: A mathematical model publication-title: J R Soc Interface contributor: fullname: Hargrove – volume: 70 start-page: 1163 year: 2008 end-page: 1191 ident: bib0009 article-title: Tuberculosis transmission model with chemoprophylaxis and treatment publication-title: Bull Math Biol contributor: fullname: Zimba – year: 1981 ident: bib0014 publication-title: Applications centre manifold theory contributor: fullname: Carr – volume: 273 start-page: 497 year: 1996 end-page: 500 ident: bib0011 article-title: Control strategies for tuberculosis epidemics: New method for old problem publication-title: Science contributor: fullname: Hopewell – volume: 215 start-page: 227 year: 2002 end-page: 237 ident: bib0001 article-title: Markers of disease evolution: The case of tuberculosis publication-title: J Theor Biol contributor: fullname: Castillo-Chavez – volume: 64 start-page: 260 year: 2003 end-page: 276 ident: bib0002 article-title: Global result for an epidemic model with vaccination that exihibits backward bifurcation publication-title: SIAM J Appl Math contributor: fullname: van den Driessche – volume: vol. 1 start-page: 33 year: 1995 end-page: 50 ident: bib0017 article-title: Asymptotically autonomous epidemic models publication-title: Mathematical population dynamics: Analysis of heterogeneity theory of epidemics contributor: fullname: Thieme – volume: 298 start-page: 418 year: 2004 end-page: 431 ident: bib0012 article-title: Backward bifurcation in simple vaccination models publication-title: J Math Anal Appl contributor: fullname: Brauer – year: 2010 ident: bib0041 article-title: Rapport sur la présentation des résultats définitifs contributor: fullname: NIS – volume: 39 start-page: 2213 year: 2001 end-page: 2218 ident: bib0005 article-title: Molecular epidemiology study of exogenous reinfection in an area with a low incidence of tuberculosis publication-title: J Clin Microbiol contributor: fullname: Molteni – volume: 282 start-page: 677 year: 1999 end-page: 686 ident: bib0019 article-title: For the who global surveillance and monitoring project: Global burden of tuberculosis estimated incidence and prevalence and mortality by country publication-title: JAMA contributor: fullname: Raviglione – volume: 209 start-page: 51 year: 2007 end-page: 75 ident: bib0026 article-title: Stability analysis of within-host parasite models with delays publication-title: Math Biosci contributor: fullname: Sallet – volume: 20 start-page: 986 year: 2015 end-page: 1003 ident: bib0035 article-title: Optimal control for a tuberculosis model with undetected cases in cameroon publication-title: Commun Nonlinear Sci Numer Simul contributor: fullname: Deuflhard – volume: 68 start-page: 577 year: 2006 end-page: 614 ident: bib0021 article-title: Theoretical assesssment of public health impact of imperfect prophylatics HIV-1 vaccines with therapeutic benefits publication-title: Bull Math Biol contributor: fullname: Gumel – volume: 11 start-page: 276 year: 2011 ident: bib0004 article-title: Analysis of undiagnosed tuberculosis-related deaths identified at post-mortem among HIV-infected patients in Russia: A descriptive study publication-title: BMC Infect Dis contributor: fullname: Fedyukovitch – volume: 2 start-page: 100 year: 2005 end-page: 102 ident: bib0008 article-title: Global health challenges: The need for an expanded discourse on bioethics publication-title: Public Libr Sci Med PLOS contributor: fullname: Singer – volume: 1 start-page: 81 year: 2004 end-page: 91 ident: bib0044 article-title: Influence of backward bifurcation on interpretation of publication-title: Math Biosci Eng contributor: fullname: Kirchner – volume: 2 start-page: 101 year: 2007 end-page: 113 ident: bib0043 article-title: Dynamics of tuberculosis: The effect of direct observation therapy strategy (dots) in nigeria publication-title: Math Mod Nat Phen contributor: fullname: Korobeinikov – volume: 57 start-page: 235 year: 2000 end-page: 247 ident: bib0022 article-title: A model for tuberculosis with exogenous reinfection publication-title: Theor Popul Biol contributor: fullname: Capurro – volume: 328 start-page: 856 year: 2010 end-page: 861 ident: bib0020 article-title: The population dynamics and control of tuberculosis publication-title: Science contributor: fullname: Williams – volume: 175 start-page: 87 year: 2007 end-page: 93 ident: bib0051 article-title: Undiagnosed tuberculosis in a community with high HIV prevalence: implications for tuberculosis control publication-title: Am J Respir Crit Care Med contributor: fullname: Whitelaw – volume: 35 start-page: 629 year: 1997 end-page: 635 ident: bib0015 article-title: To treat or not to treat: The case of tuberculosis publication-title: J Math Biol contributor: fullname: Feng – volume: 65 start-page: 6 year: 1990 end-page: 24 ident: bib0039 article-title: Tuberculosis in developing countries: Burden, intervention, and cost publication-title: Bull Int Union Tuberc Lung Dis contributor: fullname: Rouillon – year: 2001 ident: bib0013 publication-title: Mathematical models in population biology and epidemiology contributor: fullname: Castillo-Chavez – volume: 42 start-page: 599 year: 2000 end-page: 653 ident: bib0024 article-title: The mathematics of infectious diseases publication-title: SIAM Rev contributor: fullname: Hethcote – volume: 164 start-page: 183 year: 2000 end-page: 201 ident: bib0030 article-title: A simple vaccination model with multiple endemic states publication-title: Math Biosci contributor: fullname: Halesco-Hernandez – ident: 10.1016/j.cnsns.2016.04.012_bib0040 – volume: 180 start-page: 28 year: 2002 ident: 10.1016/j.cnsns.2016.04.012_bib0046 article-title: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission publication-title: Math Biosci doi: 10.1016/S0025-5564(02)00108-6 contributor: fullname: van den Driessche – volume: 282 start-page: 677 year: 1999 ident: 10.1016/j.cnsns.2016.04.012_bib0019 article-title: For the who global surveillance and monitoring project: Global burden of tuberculosis estimated incidence and prevalence and mortality by country publication-title: JAMA doi: 10.1001/jama.282.7.677 contributor: fullname: Dye – volume: 68 start-page: 577 year: 2006 ident: 10.1016/j.cnsns.2016.04.012_bib0021 article-title: Theoretical assesssment of public health impact of imperfect prophylatics HIV-1 vaccines with therapeutic benefits publication-title: Bull Math Biol doi: 10.1007/s11538-005-9057-5 contributor: fullname: Elbasha – volume: 64 start-page: 260 year: 2003 ident: 10.1016/j.cnsns.2016.04.012_bib0002 article-title: Global result for an epidemic model with vaccination that exihibits backward bifurcation publication-title: SIAM J Appl Math doi: 10.1137/S0036139902413829 contributor: fullname: Arino – volume: 1 start-page: 361 year: 2004 ident: 10.1016/j.cnsns.2016.04.012_bib0016 article-title: Dynamical models of tuberculosis and their applications publication-title: Math Biosci Eng doi: 10.3934/mbe.2004.1.361 contributor: fullname: Castillo-Chavez – volume: 29 start-page: 1097 issue: 5-6 year: 2011 ident: 10.1016/j.cnsns.2016.04.012_bib0032 article-title: Global properties of a tuberculosis model with nlatents classes publication-title: JAMI contributor: fullname: Moualeu – year: 2010 ident: 10.1016/j.cnsns.2016.04.012_sbref0040 contributor: fullname: NIS – volume: 1 start-page: 506 year: 2007 ident: 10.1016/j.cnsns.2016.04.012_bib0027 article-title: Multi-compartment models publication-title: Discret Contin Dyn Syst Ser B contributor: fullname: Iggidr – volume: 215 start-page: 227 year: 2002 ident: 10.1016/j.cnsns.2016.04.012_bib0001 article-title: Markers of disease evolution: The case of tuberculosis publication-title: J Theor Biol doi: 10.1006/jtbi.2001.2489 contributor: fullname: Aparicio – volume: 171 start-page: 1430 year: 2005 ident: 10.1016/j.cnsns.2016.04.012_bib0048 article-title: Rate of reinfection tuberculosis after successful treatment is higher than rate of new tuberculosis publication-title: Am J Respir Crit Care Med doi: 10.1164/rccm.200409-1200OC contributor: fullname: Verver – year: 2001 ident: 10.1016/j.cnsns.2016.04.012_bib0013 contributor: fullname: Brauer – volume: 328 start-page: 856 issue: 5980 year: 2010 ident: 10.1016/j.cnsns.2016.04.012_bib0020 article-title: The population dynamics and control of tuberculosis publication-title: Science doi: 10.1126/science.1185449 contributor: fullname: Dye – volume: 70 start-page: 1163 issue: 4 year: 2008 ident: 10.1016/j.cnsns.2016.04.012_bib0009 article-title: Tuberculosis transmission model with chemoprophylaxis and treatment publication-title: Bull Math Biol doi: 10.1007/s11538-008-9295-4 contributor: fullname: Bhunu – year: 1981 ident: 10.1016/j.cnsns.2016.04.012_bib0014 contributor: fullname: Carr – volume: vol. 1 start-page: 33 year: 1995 ident: 10.1016/j.cnsns.2016.04.012_bib0017 article-title: Asymptotically autonomous epidemic models contributor: fullname: Castillo-Chavez – volume: 5 start-page: 819 year: 2005 ident: 10.1016/j.cnsns.2016.04.012_bib0042 article-title: Tuberculosis control in the era of HIV publication-title: Nat Rev Immunol doi: 10.1038/nri1704 contributor: fullname: Nunn – volume: 341 start-page: 1174 year: 1999 ident: 10.1016/j.cnsns.2016.04.012_bib0047 article-title: Exogenous reinfection as a cause of recurrent tuberculosis after curative treatment publication-title: N Engl J Med doi: 10.1056/NEJM199910143411602 contributor: fullname: van Rie – volume: 209 start-page: 51 year: 2007 ident: 10.1016/j.cnsns.2016.04.012_bib0026 article-title: Stability analysis of within-host parasite models with delays publication-title: Math Biosci doi: 10.1016/j.mbs.2007.01.008 contributor: fullname: Iggidr – volume: 19 start-page: 113 year: 2002 ident: 10.1016/j.cnsns.2016.04.012_bib0052 article-title: The effects of re-infection in directly transmitted infections modeled with vaccination publication-title: IMA J Math Appl Med Biol doi: 10.1093/imammb/19.2.113 contributor: fullname: Yang – volume: 129 start-page: 147 year: 2002 ident: 10.1016/j.cnsns.2016.04.012_bib0006 article-title: A clarification of transmission terms in host-microparasite models : Numbers, densities and areas publication-title: Epidemiol Infect doi: 10.1017/S0950268802007148 contributor: fullname: Begon – volume: 7 start-page: 117 issue: 03 year: 2012 ident: 10.1016/j.cnsns.2016.04.012_bib0033 article-title: Analysis of the impact of diabetes on the dynamics transmission of tuberculosis publication-title: Math Model Nat Phenom doi: 10.1051/mmnp/20127309 contributor: fullname: Moualeu – volume: 146 start-page: 15 year: 1997 ident: 10.1016/j.cnsns.2016.04.012_bib0023 article-title: Backward bifurcation in epidemic control publication-title: Math Biosci doi: 10.1016/S0025-5564(97)00027-8 contributor: fullname: Hadeler – volume: 15 start-page: 322 year: 2006 ident: 10.1016/j.cnsns.2016.04.012_bib0007 article-title: Facing ethical challenges in rolling out antiretroviral treatment in resource-poor countries: Comment on “they call it ‘patient selection’ in khayelitsha” publication-title: Camb Q Healthc Eth contributor: fullname: Benatar – volume: 213 start-page: 1 issue: 1 year: 2008 ident: 10.1016/j.cnsns.2016.04.012_bib0028 article-title: Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE) publication-title: Math Biosci doi: 10.1016/j.mbs.2008.02.005 contributor: fullname: Kamgang – year: 2007 ident: 10.1016/j.cnsns.2016.04.012_sbref0031 contributor: fullname: Kumar – volume: 175 start-page: 87 issue: 1 year: 2007 ident: 10.1016/j.cnsns.2016.04.012_bib0051 article-title: Undiagnosed tuberculosis in a community with high HIV prevalence: implications for tuberculosis control publication-title: Am J Respir Crit Care Med doi: 10.1164/rccm.200606-759OC contributor: fullname: Wood – volume: 35 start-page: 629 year: 1997 ident: 10.1016/j.cnsns.2016.04.012_bib0015 article-title: To treat or not to treat: The case of tuberculosis publication-title: J Math Biol doi: 10.1007/s002850050069 contributor: fullname: Castillo-Chavez – year: 2012 ident: 10.1016/j.cnsns.2016.04.012_sbref0049 contributor: fullname: WHO – volume: 2 start-page: 100 issue: 7 year: 2005 ident: 10.1016/j.cnsns.2016.04.012_bib0008 article-title: Global health challenges: The need for an expanded discourse on bioethics publication-title: Public Libr Sci Med PLOS contributor: fullname: Benatar – volume: 273 start-page: 497 year: 1996 ident: 10.1016/j.cnsns.2016.04.012_bib0011 article-title: Control strategies for tuberculosis epidemics: New method for old problem publication-title: Science doi: 10.1126/science.273.5274.497 contributor: fullname: Blower – volume: 201 start-page: 58 year: 2006 ident: 10.1016/j.cnsns.2016.04.012_bib0049 article-title: Backward bifurcation of an epidemic model with treatment publication-title: Math Biosci doi: 10.1016/j.mbs.2005.12.022 contributor: fullname: Wang – year: 2013 ident: 10.1016/j.cnsns.2016.04.012_bib0036 contributor: fullname: Moualeu-Ngangue – volume: 1 start-page: 260 year: 2007 ident: 10.1016/j.cnsns.2016.04.012_bib0025 article-title: Global analysis of new malaria intrahost models with a competitive exclusion principle publication-title: SIAM J Appl Math contributor: fullname: Iggidr – volume: 353 start-page: 997 year: 1999 ident: 10.1016/j.cnsns.2016.04.012_bib0018 article-title: An African perspective of tuberculosis and HIV/AIDS publication-title: Lancet doi: 10.1016/S0140-6736(99)01141-1 contributor: fullname: Chintu – volume: 10 start-page: e0120607 issue: 4 year: 2015 ident: 10.1016/j.cnsns.2016.04.012_bib0037 article-title: Parameter identification in a tuberculosis model for cameroon publication-title: PloS One doi: 10.1371/journal.pone.0120607 contributor: fullname: Moualeu-Ngangue – volume: 11 start-page: 433 year: 2012 ident: 10.1016/j.cnsns.2016.04.012_bib0029 article-title: Global dynamics of a tuberculosis epidemic model and the influence of backward bifurcation publication-title: J Math Model Algorithm doi: 10.1007/s10852-012-9210-8 contributor: fullname: Kar – volume: 42 start-page: 599 year: 2000 ident: 10.1016/j.cnsns.2016.04.012_bib0024 article-title: The mathematics of infectious diseases publication-title: SIAM Rev doi: 10.1137/S0036144500371907 contributor: fullname: Hethcote – volume: 19 start-page: 683 issue: 04 year: 2011 ident: 10.1016/j.cnsns.2016.04.012_bib0034 article-title: Modeling and analysis of HIV and hepatitis cco-infections publication-title: J Biol Syst doi: 10.1142/S0218339011004159 contributor: fullname: Moualeu – volume: 1 start-page: 81 issue: 1 year: 2004 ident: 10.1016/j.cnsns.2016.04.012_bib0044 article-title: Influence of backward bifurcation on interpretation of R0 in a model of epidemic tuberculosis with reinfection publication-title: Math Biosci Eng doi: 10.3934/mbe.2004.1.81 contributor: fullname: Singer – volume: 65 start-page: 6 year: 1990 ident: 10.1016/j.cnsns.2016.04.012_bib0039 article-title: Tuberculosis in developing countries: Burden, intervention, and cost publication-title: Bull Int Union Tuberc Lung Dis contributor: fullname: Murray – volume: 223 start-page: 391 year: 2003 ident: 10.1016/j.cnsns.2016.04.012_bib0038 article-title: On the treatment of tuberculosis in hetergeneous populations publication-title: J Theor Biol doi: 10.1016/S0022-5193(03)00038-9 contributor: fullname: Murphy – volume: 6 start-page: 11 year: 2009 ident: 10.1016/j.cnsns.2016.04.012_bib0045 article-title: Tuberculosis reinfection rate as a proportion of total infection rate correlates with the logarithm of the incidence rate: A mathematical model publication-title: J R Soc Interface doi: 10.1098/rsif.2008.0184 contributor: fullname: Uys – volume: 39 start-page: 2213 year: 2001 ident: 10.1016/j.cnsns.2016.04.012_bib0005 article-title: Molecular epidemiology study of exogenous reinfection in an area with a low incidence of tuberculosis publication-title: J Clin Microbiol doi: 10.1128/JCM.39.6.2213-2218.2001 contributor: fullname: Bandera – volume: 298 start-page: 418 year: 2004 ident: 10.1016/j.cnsns.2016.04.012_bib0012 article-title: Backward bifurcation in simple vaccination models publication-title: J Math Anal Appl doi: 10.1016/j.jmaa.2004.05.045 contributor: fullname: Brauer – year: 1978 ident: 10.1016/j.cnsns.2016.04.012_bib0010 contributor: fullname: Birkhoff – volume: 2 start-page: 101 year: 2007 ident: 10.1016/j.cnsns.2016.04.012_bib0043 article-title: Dynamics of tuberculosis: The effect of direct observation therapy strategy (dots) in nigeria publication-title: Math Mod Nat Phen contributor: fullname: Okuonghae – volume: 20 start-page: 986 issue: 3 year: 2015 ident: 10.1016/j.cnsns.2016.04.012_bib0035 article-title: Optimal control for a tuberculosis model with undetected cases in cameroon publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2014.06.037 contributor: fullname: Moualeu – volume: 57 start-page: 235 issue: 3 year: 2000 ident: 10.1016/j.cnsns.2016.04.012_bib0022 article-title: A model for tuberculosis with exogenous reinfection publication-title: Theor Popul Biol doi: 10.1006/tpbi.2000.1451 contributor: fullname: Feng – volume: 57 start-page: 557 issue: 4 year: 2008 ident: 10.1016/j.cnsns.2016.04.012_bib0003 article-title: Modeling the joint epidemics of TB and HIV in a South African township publication-title: J Math Biol doi: 10.1007/s00285-008-0177-z contributor: fullname: Bacaër – volume: 11 start-page: 276 issue: 1 year: 2011 ident: 10.1016/j.cnsns.2016.04.012_bib0004 article-title: Analysis of undiagnosed tuberculosis-related deaths identified at post-mortem among HIV-infected patients in Russia: A descriptive study publication-title: BMC Infect Dis doi: 10.1186/1471-2334-11-276 contributor: fullname: Balabanova – volume: 164 start-page: 183 year: 2000 ident: 10.1016/j.cnsns.2016.04.012_bib0030 article-title: A simple vaccination model with multiple endemic states publication-title: Math Biosci doi: 10.1016/S0025-5564(00)00003-1 contributor: fullname: Kribs-Zaleta |
| SSID | ssj0016954 |
| Score | 2.2888536 |
| Snippet | •A tuberculosis model with undetected infectious and lost-sight cases is analyzed.•The model exhibits the phenomenon of backward bifurcation.•Backward... A deterministic model of tuberculosis (TB) in sub-Saharan Africa including undetected and lost-sight cases is presented and analyzed. The model is shown to... |
| SourceID | hal proquest crossref elsevier |
| SourceType | Open Access Repository Aggregation Database Publisher |
| StartPage | 48 |
| SubjectTerms | Bifurcation Bifurcations Computer simulation Gain Mathematical models Mathematics Mycobacterium Nonlinear dynamical systems Perturbation methods Reproduction Stability Tuberculosis Unity |
| Title | Analysis of a tuberculosis model with undetected and lost-sight cases |
| URI | https://dx.doi.org/10.1016/j.cnsns.2016.04.012 https://search.proquest.com/docview/1825543245 https://search.proquest.com/docview/1827926664 https://hal.sorbonne-universite.fr/hal-01317636 |
| Volume | 41 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB7c9eLFt7i-iOLRuH2kaXpcRFmfFxW8hSRNUZGu2K5Hf7sz3VZQ0IPQS9OEhi_JzJfO9AvAoZImj6VJeeptygXOGG4jUfAszY0LpA2SJqJ7fSPH9-LiIXmYg5PuXxhKq2xt_8ymN9a6LRm2aA5fn56GtxTfT9KAGAWx-qwH8-iOItWH-dH55fjmK5ggs-YwNKrPqUEnPtSkebmyKkm2O5SN5GkY_eageo-UKfnDYDde6GwZFlv6yEazHq7AnC9XYamlkqxdqNUanHZiI2xSMMPqqfVvbvoyoZLm8BtGH2AZ_UFGUQRsa8qc4fOaV7RdZw69W7UO92endydj3p6YwB1us2runEU0rEnRaRtrg9za2GcxKbwQsyhEYp3LVOQM7qGdy10ReYWX8HEUG_RnG9AvJ6XfBBb4yKaZVLEJrVC5UCbOiiRxRsVB4b0awFEHk36dCWPoLmPsWTeoakJVB0IjqgOQHZT62_hqNN1_NzxA4L9eQWrY49GVpjKSCkLzKN_DAex346JxeVDMw5R-Mq00bp-QMCFrTP6sk2ZIVKTY-m8vt2GB7mZ5LjvQr9-mfhfZSm33oHf8Ee61c_ITedbotQ |
| link.rule.ids | 230,315,783,787,888,4509,24128,27936,27937,45597,45691 |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB58HPTiW1yfUTwattumaXNcRKm67kUFbyFJU1SkK7br73em2woKehB6yoOWL8nMl87kC8BpKk0eSZPwxNuEC5wx3Iai4CrJjQukDeImons7ltmDuH6MH-fgvDsLQ2mVre2f2fTGWrcl_RbN_tvzc_-O4vtxEhCjIFav5mER2YDC1bk4vLrJxl_BBKmay9CoPacOnfhQk-blyqok2e6BbCRPB-FvDmr-iTIlfxjsxgtdrsFKSx_ZcPaF6zDnyw1YbakkaxdqtQkXndgImxTMsHpq_bubvk6opLn8htEPWEYnyCiKgH1NmTOsr3lF23Xm0LtVW_BweXF_nvH2xgTucJtVc-csomFNgk7bWBvk1kZeRaTwQsyiELF1TqWhM7iHdi53RehTfISPwsigP9uGhXJS-h1ggQ9tomQamYEVaS5SE6kijp1Jo6DwPu3BWQeTfpsJY-guY-xFN6hqQlUHQiOqPZAdlPrb-Go03X93PEHgv15BatjZcKSpjKSC0DzKj0EPjrtx0bg8KOZhSj-ZVhq3T0iYkDXGf7ZJFBIVKXb_-5VHsJTd34706Gp8swfLVDPLedmHhfp96g-QudT2sJ2ZnxyZ6qk |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Analysis+of+a+tuberculosis+model+with+undetected+and+lost-sight+cases&rft.jtitle=Communications+in+nonlinear+science+%26+numerical+simulation&rft.au=Moualeu%2C+D.P.&rft.au=Nana+Yakam%2C+A.&rft.au=Bowong%2C+S.&rft.au=Temgoua%2C+A.&rft.date=2016-12-01&rft.pub=Elsevier&rft.issn=1007-5704&rft.eissn=1878-7274&rft.volume=41&rft_id=info:doi/10.1016%2Fj.cnsns.2016.04.012&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=oai_HAL_hal_01317636v1 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1007-5704&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1007-5704&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1007-5704&client=summon |