On a reaction–diffusion system modelling infectious diseases without lifetime immunity
In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is...
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| Published in | European journal of applied mathematics Vol. 33; no. 5; pp. 803 - 827 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge
Cambridge University Press
01.10.2022
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| Online Access | Get full text |
| ISSN | 0956-7925 1469-4425 |
| DOI | 10.1017/S0956792521000231 |
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| Abstract | In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving
a priori
estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences. |
|---|---|
| AbstractList | In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving
a priori
estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences. In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving a priori estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences. |
| Author | YIN, HONG-MING |
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| Cites_doi | 10.1038/280455a0 10.1088/1361-6544/ab8772 10.3934/dcdsb.2012.17.2829 10.1016/S0025-5564(02)00108-6 10.1007/978-1-4899-3614-1 10.1098/rspa.1927.0118 10.1007/BF00163027 10.1007/978-1-4615-3034-3 10.1137/120876642 10.1137/S0036144500371907 10.1007/BF02415082 10.1016/j.na.2017.03.007 10.3934/mbe.2011.8.733 10.1006/jdeq.1996.0157 10.1142/3302 10.1016/S0140-6736(11)60273-0 10.1016/0025-5564(92)90081-7 10.1016/S0025-5564(99)00030-9 10.3934/dcdsb.2016.21.1297 10.57262/ade/1356651736 10.1016/j.na.2017.02.022 10.1007/978-3-642-18460-4 10.1016/0022-1236(89)90005-0 10.1016/j.mbs.2011.04.001 10.1080/17513758.2014.974696 10.1080/03605300903089867 10.1038/280361a0 10.1216/JIE-1989-2-1-31 |
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| Copyright | The Author(s), 2021. Published by Cambridge University Press |
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| References | Evans (S0956792521000231_ref10) 2010; 19 S0956792521000231_ref13 Hethcote (S0956792521000231_ref11) 2000; 42 S0956792521000231_ref12 Li (S0956792521000231_ref17) 1999; 160 Lou (S0956792521000231_ref20) 1996; 131 Yamazaki (S0956792521000231_ref35) 2018; 10 Yamazaki (S0956792521000231_ref34) 2017; 14 S0956792521000231_ref19 Andrew (S0956792521000231_ref2) 2011; 377 Morgan (S0956792521000231_ref22) 2020; 33 May (S0956792521000231_ref21) 1979; 280 Yamazaki (S0956792521000231_ref33) 2016; 21 Yin (S0956792521000231_ref37) 2017; 159 Eisenberg (S0956792521000231_ref9) 2002; 180 Chadam (S0956792521000231_ref8) 1989; 2 Caceres (S0956792521000231_ref5) 2017; 159 van de Driessche (S0956792521000231_ref31) 2002; 180 Thieme (S0956792521000231_ref27) 1992; 111 Ladyzenskaja (S0956792521000231_ref16) 1968; 23 Vaidya (S0956792521000231_ref30) 2012; 17 S0956792521000231_ref23 Temam (S0956792521000231_ref25) 1988; 68 Anderson (S0956792521000231_ref1) 1979; 280 Troianiello (S0956792521000231_ref29) 1987 S0956792521000231_ref26 Shuai (S0956792521000231_ref24) 2013; 73 Kuznetsov (S0956792521000231_ref15) 1994; 32 Bocccardo (S0956792521000231_ref4) 1989; 87 Yin (S0956792521000231_ref36) 1997; 10 Campanato (S0956792521000231_ref6) 1966; 73 Wang (S0956792521000231_ref32) 2015; 9 Klements (S0956792521000231_ref14) 2020; 37 Tian (S0956792521000231_ref28) 2011; 232 Caputo (S0956792521000231_ref7) 2009; 34 Liao (S0956792521000231_ref18) 2011; 8 Bendahmane (S0956792521000231_ref3) 2002; 7 |
| References_xml | – volume: 68 volume-title: Applied Mathematical Sciences year: 1988 ident: S0956792521000231_ref25 – volume: 280 start-page: 455 year: 1979 ident: S0956792521000231_ref21 article-title: Population biology of infectious disease II publication-title: Nature doi: 10.1038/280455a0 – volume: 33 start-page: 3105 year: 2020 ident: S0956792521000231_ref22 article-title: Boundedness for reaction-diffusion systems with Lyapunov functions and intermediate sum conditions publication-title: Nonlinearity doi: 10.1088/1361-6544/ab8772 – volume: 17 start-page: 2829 year: 2012 ident: S0956792521000231_ref30 article-title: Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment publication-title: Discrete Contin. Dyn. Ser. B doi: 10.3934/dcdsb.2012.17.2829 – volume: 23 year: 1968 ident: S0956792521000231_ref16 article-title: Linear and Quasilinear Equations of Parabolic Type publication-title: AMS Translation Series – volume: 180 start-page: 29 year: 2002 ident: S0956792521000231_ref31 article-title: Reproduction numbers and sub-threshold endemic equilibra for compartmental models of disease transmission publication-title: Math. Biosci. doi: 10.1016/S0025-5564(02)00108-6 – volume-title: Elliptic Differential Equations and Obstacle Problems year: 1987 ident: S0956792521000231_ref29 doi: 10.1007/978-1-4899-3614-1 – ident: S0956792521000231_ref13 doi: 10.1098/rspa.1927.0118 – volume: 180 start-page: 29 year: 2002 ident: S0956792521000231_ref9 article-title: A Cholera model in a patchy environment with water and human movement publication-title: Math. Biosci. – volume: 32 start-page: 109 year: 1994 ident: S0956792521000231_ref15 article-title: Bifurcation analysis of periodic SEIR and SIR epidemic models publication-title: J. Math. Biol. doi: 10.1007/BF00163027 – ident: S0956792521000231_ref23 doi: 10.1007/978-1-4615-3034-3 – volume: 73 start-page: 1513 year: 2013 ident: S0956792521000231_ref24 article-title: Global stability of infectious disease models using lyapunov functions publication-title: SIAM J. Appl. Math. doi: 10.1137/120876642 – volume: 42 start-page: 599 year: 2000 ident: S0956792521000231_ref11 article-title: The mathematics of infectious diseases publication-title: SIAM Rev. doi: 10.1137/S0036144500371907 – ident: S0956792521000231_ref26 – volume: 73 start-page: 55 year: 1966 ident: S0956792521000231_ref6 article-title: Equazioni paraboliche del second ordine e space publication-title: Ann. Math. Pura Appl. doi: 10.1007/BF02415082 – volume: 10 start-page: 200 year: 2018 ident: S0956792521000231_ref35 article-title: Global well-posedness of infectious disease models without life-time immunity: the cases of Cholera and avian influenza publication-title: Math. Med. Biol. – volume: 159 start-page: 62 year: 2017 ident: S0956792521000231_ref5 article-title: Close-to-equilibrium behavior of quadratic reaction-diffusion systems with detailed balance publication-title: Nonlinear Anal. doi: 10.1016/j.na.2017.03.007 – volume: 8 start-page: 733 year: 2011 ident: S0956792521000231_ref18 article-title: Stability analysis and application of a mathematical cholera model publication-title: Math. Biosci. Eng. doi: 10.3934/mbe.2011.8.733 – volume: 131 start-page: 791 year: 1996 ident: S0956792521000231_ref20 article-title: Diffusion, self-diffusion and cross-diffusion publication-title: J. Differ. Equations doi: 10.1006/jdeq.1996.0157 – ident: S0956792521000231_ref19 doi: 10.1142/3302 – volume: 19 volume-title: AMS Graduate Studies in Mathematics year: 2010 ident: S0956792521000231_ref10 – volume: 377 start-page: 1248 year: 2011 ident: S0956792521000231_ref2 article-title: Transmission dynamics and control of cholera in Haiti: an epidemic model publication-title: Lancet doi: 10.1016/S0140-6736(11)60273-0 – volume: 111 start-page: 99 year: 1992 ident: S0956792521000231_ref27 article-title: Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations publication-title: Math. Biosci. doi: 10.1016/0025-5564(92)90081-7 – volume: 160 start-page: 191 year: 1999 ident: S0956792521000231_ref17 article-title: Liancheng Wang and, Janos Karsai, Global dynamics of a SEIR model with varying total population size publication-title: Math. Biosci. doi: 10.1016/S0025-5564(99)00030-9 – volume: 21 start-page: 1297 year: 2016 ident: S0956792521000231_ref33 article-title: Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion Cholera epidemic model publication-title: Discrete Contin. Dyn. Syst. Ser. B doi: 10.3934/dcdsb.2016.21.1297 – volume: 7 start-page: 743 year: 2002 ident: S0956792521000231_ref3 article-title: Existence of solutions for reaction-diffusion systems with publication-title: Adv. Differ. Equations doi: 10.57262/ade/1356651736 – volume: 10 start-page: 31 year: 1997 ident: S0956792521000231_ref36 article-title: $L^{2,u}$ publication-title: J. Partial Differ. Equations – volume: 159 start-page: 482 year: 2017 ident: S0956792521000231_ref37 article-title: On a cross-diffusion system modeling vegetation spots and strips in a semi-arid or arid landscape publication-title: Nonlinear Anal. doi: 10.1016/j.na.2017.02.022 – ident: S0956792521000231_ref12 doi: 10.1007/978-3-642-18460-4 – volume: 37 start-page: 281 year: 2020 ident: S0956792521000231_ref14 article-title: Global classical solutions to quadratic systems with mass control in arbitrary dimensions publication-title: Ann. I. H. Poincare AN – volume: 87 start-page: 149 year: 1989 ident: S0956792521000231_ref4 article-title: Nonlinear elliptic and parabolic equations involving measure data publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(89)90005-0 – volume: 232 start-page: 31 year: 2011 ident: S0956792521000231_ref28 article-title: Global stability for Cholera epidemic models publication-title: Math. Biosci. doi: 10.1016/j.mbs.2011.04.001 – volume: 9 start-page: 233 year: 2015 ident: S0956792521000231_ref32 article-title: Analysis of Cholera epidemics with bacterial growth and spatial movement publication-title: J. Biol. Dyn. doi: 10.1080/17513758.2014.974696 – volume: 34 start-page: 1228 year: 2009 ident: S0956792521000231_ref7 article-title: Global regularity of solutions to systems of reaction-diffusion with sub-quadratic growth in any space dimension publication-title: Commun. Partial Differ. Equations doi: 10.1080/03605300903089867 – volume: 14 start-page: 559 year: 2017 ident: S0956792521000231_ref34 article-title: Global stability and uniform persistence of the reaction-convection-diffusion Cholera epidemic model publication-title: Math. Biosci. Eng. – volume: 280 start-page: 361 year: 1979 ident: S0956792521000231_ref1 article-title: Population biology of infectious diseases I publication-title: Nature doi: 10.1038/280361a0 – volume: 2 start-page: 31 year: 1989 ident: S0956792521000231_ref8 article-title: An iteration procedure for a class of integrodifferential equations of parabolic type publication-title: J. Integral Equations Appl. doi: 10.1216/JIE-1989-2-1-31 |
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| SubjectTerms | Applied mathematics Asymptotic properties Bacteria Biological models (mathematics) Cholera Coronaviruses COVID-19 Elliptic functions Energy methods Epidemics Immunity Infectious diseases Influenza Mathematical models Medical research Pandemics Partial differential equations Viruses |
| Title | On a reaction–diffusion system modelling infectious diseases without lifetime immunity |
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