Complex dynamics in an eco-epidemiological model with the cost of anti-predator behaviors
In this paper, we investigate the complex dynamics of a predator–prey model with disease in the prey, which is characterized by the reduction of prey growth rate due to the anti-predator behavior. The value of this study lies in two aspects: Mathematically, it provides the existence and the stabilit...
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| Published in | Nonlinear dynamics Vol. 107; no. 3; pp. 3127 - 3141 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.02.2022
Springer Nature B.V |
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| Abstract | In this paper, we investigate the complex dynamics of a predator–prey model with disease in the prey, which is characterized by the reduction of prey growth rate due to the anti-predator behavior. The value of this study lies in two aspects: Mathematically, it provides the existence and the stability of the equilibria and gives the existence of Hopf bifurcation. And epidemiologically, we find that the influence of the fear factor is complex: (i) The level of the population density decreases with the increasing of the fear factor; (ii) the cost of fear can destabilize the stability and benefit the emergency of the periodic behavior; and (iii) the high level of fear can induce the extinction of the predator. These results may enrich the dynamics of the eco-epidemiological systems. |
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| AbstractList | In this paper, we investigate the complex dynamics of a predator–prey model with disease in the prey, which is characterized by the reduction of prey growth rate due to the anti-predator behavior. The value of this study lies in two aspects: Mathematically, it provides the existence and the stability of the equilibria and gives the existence of Hopf bifurcation. And epidemiologically, we find that the influence of the fear factor is complex: (i) The level of the population density decreases with the increasing of the fear factor; (ii) the cost of fear can destabilize the stability and benefit the emergency of the periodic behavior; and (iii) the high level of fear can induce the extinction of the predator. These results may enrich the dynamics of the eco-epidemiological systems. |
| Author | Yao, Ruoxia Cai, Yongli Wang, Weiming Tan, Yiping Hu, Maolin |
| Author_xml | – sequence: 1 givenname: Yiping surname: Tan fullname: Tan, Yiping organization: School of Computer Science, Shaanxi Normal University, School of Mathematics and Statistics, Huaiyin Normal University – sequence: 2 givenname: Yongli surname: Cai fullname: Cai, Yongli organization: School of Mathematics and Statistics, Huaiyin Normal University – sequence: 3 givenname: Ruoxia surname: Yao fullname: Yao, Ruoxia email: rxyao@snnu.edu.cn organization: School of Computer Science, Shaanxi Normal University – sequence: 4 givenname: Maolin surname: Hu fullname: Hu, Maolin organization: School of Mathematics and Statistics, Huaiyin Normal University – sequence: 5 givenname: Weiming surname: Wang fullname: Wang, Weiming email: weimingwang2003@163.com organization: School of Mathematics and Statistics, Huaiyin Normal University |
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| Cites_doi | 10.1016/j.amc.2019.03.034 10.2307/1313225 10.1111/j.1365-2656.2009.01552.x 10.1142/S0218127418501407 10.1142/S0218127419501852 10.1142/S0218127420502107 10.1002/mma.815 10.1063/1.5111121 10.3934/mbe.2019017 10.1007/s12190-017-1142-z 10.1016/j.chaos.2014.11.010 10.1002/mma.1071 10.1016/j.apm.2018.07.021 10.1016/j.tree.2007.12.004 10.1016/S0025-5564(02)00108-6 10.1007/978-3-662-08542-4 10.1890/090226 10.1007/s11538-013-9880-z 10.1007/BF00178324 10.1016/j.jtbi.2008.08.018 10.1016/j.jfranklin.2020.07.002 10.1126/science.284.5411.28 10.1142/S0218127419501955 10.1016/j.tpb.2019.07.016 10.1007/BF00276947 10.1016/j.ecocom.2013.06.002 10.1007/s11538-017-0287-0 10.1016/j.cnsns.2020.105223 10.1126/science.1210908 10.1016/j.jde.2006.08.001 10.1007/s00285-016-0989-1 10.1007/s002850050105 10.1016/j.tpb.2004.06.010 10.1016/S0025-5564(01)00049-9 10.2307/2265536 10.1051/mmnp/201611104 10.1016/j.mbs.2008.07.011 10.1016/S0096-3003(01)00156-4 10.1016/j.ecocom.2015.01.002 |
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| Keywords | Eco-epidemiological model Hopf bifurcation Extinction Fear factor |
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| References | Bulai, Hilker (CR3) 2019; 130 Creel, Christianson (CR7) 2008; 23 Zanette, White, Allen, Michael (CR40) 2011; 334 Ko, Ryu (CR15) 2006; 231 Sieber, Malchow, Hilker (CR29) 2014; 8 Malchow, Petrovskii, Venturino (CR21) 2008 Hethcote, Wang, Han, Ma (CR12) 2004; 66 Wang, Zou (CR36) 2017; 79 Xiao, Chen (CR39) 2002; 131 Krishchenko, Starkov (CR16) 2020; 85 Sharma, Samanta (CR27) 2015; 70 Greenhalgh, Haque (CR9) 2007; 30 Kaiser (CR14) 1999; 284 Venturino, Volpert (CR32) 2016; 11 Bairagi, Adak (CR1) 2015; 22 Peterson, Page (CR23) 1987; 1 Wirsing, Ripple (CR37) 2011; 9 Haque, Jin, Venturino (CR11) 2009; 32 Lafferty, Morris (CR19) 1996; 77 Sheriff, Krebs, Boonstra (CR28) 2009; 78 Van den Driessche, Watmough (CR31) 2002; 180 Bate, Hilker (CR2) 2013; 75 Kuang, Beretta (CR17) 1998; 36 Qiao, Cai, Fu, Wang (CR24) 2019; 29 Cai, Gui, Zhang, Shi, Wang (CR5) 2018; 28 Wang, Tan, Cai, Wang (CR34) 2020; 30 Diekmann, Heesterbeek, Metz (CR8) 1990; 28 Lima (CR20) 1998; 48 Xiao, Chen (CR38) 2001; 171 Murray (CR22) 1993 Buonomo, d’Onofrio, Lacitignola (CR4) 2008; 216 Hadeler, Freedman (CR10) 1989; 27 Zhang, Cai, Fu, Wang (CR41) 2019; 356 Wang, Cai, Fu, Wang (CR33) 2019; 29 Cai, Li, Kang, Wang, Wang (CR6) 2020; 357 Upadhyay, Mishra (CR30) 2018; 16 Sasmal (CR25) 2018; 64 Wang, Zanette, Zou (CR35) 2016; 73 Shaikh, Das, Ali (CR26) 2018; 58 Hilker, Schmitz (CR13) 2008; 255 Kumar, Dubey (CR18) 2019; 29 Y Kuang (7133_CR17) 1998; 36 KD Lafferty (7133_CR19) 1996; 77 X Wang (7133_CR36) 2017; 79 AJ Wirsing (7133_CR37) 2011; 9 IM Bulai (7133_CR3) 2019; 130 LS Lima (7133_CR20) 1998; 48 AM Bate (7133_CR2) 2013; 75 JD Murray (7133_CR22) 1993 RO Peterson (7133_CR23) 1987; 1 D Greenhalgh (7133_CR9) 2007; 30 LY Zanette (7133_CR40) 2011; 334 O Diekmann (7133_CR8) 1990; 28 S Creel (7133_CR7) 2008; 23 R Upadhyay (7133_CR30) 2018; 16 P Van den Driessche (7133_CR31) 2002; 180 T Qiao (7133_CR24) 2019; 29 HW Hethcote (7133_CR12) 2004; 66 AP Krishchenko (7133_CR16) 2020; 85 W Ko (7133_CR15) 2006; 231 Y Cai (7133_CR6) 2020; 357 J Wang (7133_CR33) 2019; 29 X Wang (7133_CR34) 2020; 30 FM Hilker (7133_CR13) 2008; 255 M Sieber (7133_CR29) 2014; 8 Y Cai (7133_CR5) 2018; 28 N Bairagi (7133_CR1) 2015; 22 Y Xiao (7133_CR39) 2002; 131 H Zhang (7133_CR41) 2019; 356 X Wang (7133_CR35) 2016; 73 M Haque (7133_CR11) 2009; 32 J Kaiser (7133_CR14) 1999; 284 A Kumar (7133_CR18) 2019; 29 B Buonomo (7133_CR4) 2008; 216 H Malchow (7133_CR21) 2008 AA Shaikh (7133_CR26) 2018; 58 KP Hadeler (7133_CR10) 1989; 27 S Sharma (7133_CR27) 2015; 70 MJ Sheriff (7133_CR28) 2009; 78 Y Xiao (7133_CR38) 2001; 171 E Venturino (7133_CR32) 2016; 11 S Sasmal (7133_CR25) 2018; 64 |
| References_xml | – volume: 231 start-page: 534 issue: 2 year: 2006 end-page: 550 ident: CR15 article-title: Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge publication-title: J. Differ. Eq. – volume: 75 start-page: 2059 year: 2013 end-page: 2078 ident: CR2 article-title: Complex dynamics in an eco-epidemiological model publication-title: Bull. Math. Biol. – volume: 11 start-page: 49 year: 2016 end-page: 90 ident: CR32 article-title: Ecoepidemiology: a more comprehensive view of population interactions publication-title: Math. Model. Nat. Phenom. – volume: 1 start-page: 771 year: 1987 end-page: 773 ident: CR23 article-title: Wolf density as a predictor of predation rate publication-title: Swed. Wild. Res. – volume: 29 start-page: 1950195 issue: 14 year: 2019 ident: CR18 article-title: Modeling the effect of fear in a prey-predator system with prey refuge and gestation delay publication-title: Inter. J. Bifur. Chaos – volume: 23 start-page: 194 issue: 4 year: 2008 end-page: 201 ident: CR7 article-title: Relationships between direct predation and risk effects publication-title: Trends Ecol. Evol. – volume: 78 start-page: 1249 issue: 6 year: 2009 end-page: 1258 ident: CR28 article-title: The sensitive hare: sublethal effects of predator stress on reproduction in snowshoe hares publication-title: J. Anim. Ecol. – volume: 73 start-page: 1179 issue: 5 year: 2016 end-page: 1204 ident: CR35 article-title: Modelling the fear effect in predator-prey interactions publication-title: J. Math. Biol. – volume: 79 start-page: 1325 issue: 6 year: 2017 end-page: 1359 ident: CR36 article-title: Modeling the fear effect in predator-prey interactions with adaptive avoidance of predators publication-title: Bull. Math. Biol. – volume: 48 start-page: 25 issue: 1 year: 1998 end-page: 34 ident: CR20 article-title: Nonlethal effects in the ecology of predator-prey interactions publication-title: Bioscience – volume: 180 start-page: 29 issue: 1 year: 2002 end-page: 48 ident: CR31 article-title: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission publication-title: Math. Biosci. – volume: 356 start-page: 328 year: 2019 end-page: 337 ident: CR41 article-title: Impact of the fear effect in a prey-predator model incorporating a prey refuge publication-title: Appl. Math. Comp. – volume: 32 start-page: 875 issue: 7 year: 2009 end-page: 898 ident: CR11 article-title: An ecoepidemiological predator-prey model with standard disease incidence publication-title: Math. Meth. Appl. Sci. – volume: 27 start-page: 609 issue: 6 year: 1989 end-page: 631 ident: CR10 article-title: Predator-prey populations with parasitic infection publication-title: J. Math. Biol. – volume: 70 start-page: 69 year: 2015 end-page: 84 ident: CR27 article-title: A Leslie-Gower predator-prey model with disease in prey incorporating a prey refuge publication-title: Chaos. Solit. Fract. – volume: 284 start-page: 28 year: 1999 end-page: 30 ident: CR14 article-title: Salton sea: Battle over a dying sea publication-title: Science – volume: 171 start-page: 59 issue: 1 year: 2001 end-page: 82 ident: CR38 article-title: Modeling and analysis of a predator-prey model with disease in the prey publication-title: Math. Biosci. – volume: 255 start-page: 299 year: 2008 end-page: 306 ident: CR13 article-title: Disease-induced stabilization of predator-prey oscillations publication-title: J. Theor. Biol. – volume: 8 start-page: 74 year: 2014 end-page: 82 ident: CR29 article-title: Disease-induced modification of prey competition in eco-epidemiological models publication-title: Ecol. Complex. – volume: 30 start-page: 2050210 issue: 14 year: 2020 ident: CR34 article-title: Impact of the fear effect on the stability and bifurcation of a leslie-gower predator-prey model publication-title: Inter. J. Bifurc. Chaos – volume: 58 start-page: 235 issue: 1–2 year: 2018 end-page: 255 ident: CR26 article-title: Study of lg-holling type iii predator-prey model with disease in predator publication-title: J. Appl. Math. Comput. – volume: 85 start-page: 105223 year: 2020 ident: CR16 article-title: Convergence dynamics in one eco-epidemiological model: Self-healing and some related results publication-title: Commun. Nonlinear Sci. – volume: 29 start-page: 1950185 year: 2019 ident: CR24 article-title: Stability and hopf bifurcation in a predator-prey model with the cost of anti-predator behaviors publication-title: Inter. J. Bifurc. Chaos – volume: 77 start-page: 1390 year: 1996 end-page: 1397 ident: CR19 article-title: Altered behavior of parasitized killifish increases susceptibility to predation by bird final hosts publication-title: Ecology – volume: 30 start-page: 911 issue: 8 year: 2007 end-page: 929 ident: CR9 article-title: A predator-prey model with disease in the prey species only publication-title: Math. Meth. Appl. Sci. – volume: 64 start-page: 1 year: 2018 end-page: 14 ident: CR25 article-title: Population dynamics with multiple Allee effects induced by fear factors induced by fear factors-a mathematical study on prey-predator publication-title: Appl. Math. Model. – volume: 130 start-page: 191 year: 2019 end-page: 202 ident: CR3 article-title: Eco-epidemiological interactions with predator interference and infection publication-title: Theor. Popul. Biol. – year: 1993 ident: CR22 publication-title: Mathematical biology – volume: 28 start-page: 1850140 year: 2018 ident: CR5 article-title: Bifurcations and pattern formation in a predator-prey model publication-title: Inter. J. Bifurc. Chaos – volume: 29 start-page: 083109 issue: 8 year: 2019 ident: CR33 article-title: The effect of the fear factor on the dynamics of a predator-prey model incorporating the prey refuge publication-title: Chaos – volume: 131 start-page: 397 issue: 2–3 year: 2002 end-page: 414 ident: CR39 article-title: A ratio-dependent predator-prey model with disease in the prey publication-title: Appl. Math. Comp. – volume: 357 start-page: 8899 year: 2020 end-page: 8924 ident: CR6 article-title: The fluctuation impact of human mobility on the influenza transmission publication-title: J. Franklin Inst. – volume: 28 start-page: 365 issue: 4 year: 1990 end-page: 382 ident: CR8 article-title: On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations publication-title: J. Math. Biol. – year: 2008 ident: CR21 publication-title: Spatiotemporal patterns in ecology and epidemiology-theory, models, and simulation – volume: 16 start-page: 338 issue: 1 year: 2018 end-page: 372 ident: CR30 article-title: Population dynamic consequences of fearful prey in a spatiotemporal predator-prey system publication-title: Math. Biosci. Eng. – volume: 36 start-page: 389 year: 1998 end-page: 406 ident: CR17 article-title: Global qualitative analysis of a ratio-dependent predator-prey system publication-title: J. Math. Biol. – volume: 9 start-page: 335 issue: 6 year: 2011 end-page: 341 ident: CR37 article-title: A comparison of shark and wolf research reveals similar behavioral responses by prey publication-title: Front. Ecol. Environ. – volume: 334 start-page: 1398 issue: 6061 year: 2011 end-page: 1401 ident: CR40 article-title: Perceived predation risk reduces the number of offspring songbirds produce per year publication-title: Science – volume: 22 start-page: 1 year: 2015 end-page: 12 ident: CR1 article-title: Complex dynamics of a predatorcpreycparasite system: an interplay among infection rate, predator’s reproductive gain and preference publication-title: Ecol. Complex. – volume: 216 start-page: 9 issue: 1 year: 2008 end-page: 16 ident: CR4 article-title: Global stability of an sir epidemic model with information dependent vaccination publication-title: Math. Biosci. – volume: 66 start-page: 259 issue: 3 year: 2004 end-page: 268 ident: CR12 article-title: A predator-prey model with infected prey publication-title: Theor. Popu. Biol. – volume: 356 start-page: 328 year: 2019 ident: 7133_CR41 publication-title: Appl. Math. Comp. doi: 10.1016/j.amc.2019.03.034 – volume: 48 start-page: 25 issue: 1 year: 1998 ident: 7133_CR20 publication-title: Bioscience doi: 10.2307/1313225 – volume: 78 start-page: 1249 issue: 6 year: 2009 ident: 7133_CR28 publication-title: J. Anim. Ecol. doi: 10.1111/j.1365-2656.2009.01552.x – volume: 28 start-page: 1850140 year: 2018 ident: 7133_CR5 publication-title: Inter. J. Bifurc. Chaos doi: 10.1142/S0218127418501407 – volume: 29 start-page: 1950185 year: 2019 ident: 7133_CR24 publication-title: Inter. J. Bifurc. Chaos doi: 10.1142/S0218127419501852 – volume: 30 start-page: 2050210 issue: 14 year: 2020 ident: 7133_CR34 publication-title: Inter. J. Bifurc. Chaos doi: 10.1142/S0218127420502107 – volume: 30 start-page: 911 issue: 8 year: 2007 ident: 7133_CR9 publication-title: Math. Meth. Appl. Sci. doi: 10.1002/mma.815 – volume: 29 start-page: 083109 issue: 8 year: 2019 ident: 7133_CR33 publication-title: Chaos doi: 10.1063/1.5111121 – volume: 16 start-page: 338 issue: 1 year: 2018 ident: 7133_CR30 publication-title: Math. Biosci. Eng. doi: 10.3934/mbe.2019017 – volume: 58 start-page: 235 issue: 1–2 year: 2018 ident: 7133_CR26 publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-017-1142-z – volume: 70 start-page: 69 year: 2015 ident: 7133_CR27 publication-title: Chaos. Solit. Fract. doi: 10.1016/j.chaos.2014.11.010 – volume: 32 start-page: 875 issue: 7 year: 2009 ident: 7133_CR11 publication-title: Math. Meth. Appl. Sci. doi: 10.1002/mma.1071 – volume: 64 start-page: 1 year: 2018 ident: 7133_CR25 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2018.07.021 – volume-title: Spatiotemporal patterns in ecology and epidemiology-theory, models, and simulation year: 2008 ident: 7133_CR21 – volume: 23 start-page: 194 issue: 4 year: 2008 ident: 7133_CR7 publication-title: Trends Ecol. Evol. doi: 10.1016/j.tree.2007.12.004 – volume: 180 start-page: 29 issue: 1 year: 2002 ident: 7133_CR31 publication-title: Math. Biosci. doi: 10.1016/S0025-5564(02)00108-6 – volume-title: Mathematical biology year: 1993 ident: 7133_CR22 doi: 10.1007/978-3-662-08542-4 – volume: 9 start-page: 335 issue: 6 year: 2011 ident: 7133_CR37 publication-title: Front. Ecol. Environ. doi: 10.1890/090226 – volume: 75 start-page: 2059 year: 2013 ident: 7133_CR2 publication-title: Bull. Math. Biol. doi: 10.1007/s11538-013-9880-z – volume: 28 start-page: 365 issue: 4 year: 1990 ident: 7133_CR8 publication-title: J. Math. Biol. doi: 10.1007/BF00178324 – volume: 255 start-page: 299 year: 2008 ident: 7133_CR13 publication-title: J. Theor. Biol. doi: 10.1016/j.jtbi.2008.08.018 – volume: 1 start-page: 771 year: 1987 ident: 7133_CR23 publication-title: Swed. Wild. Res. – volume: 357 start-page: 8899 year: 2020 ident: 7133_CR6 publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2020.07.002 – volume: 284 start-page: 28 year: 1999 ident: 7133_CR14 publication-title: Science doi: 10.1126/science.284.5411.28 – volume: 29 start-page: 1950195 issue: 14 year: 2019 ident: 7133_CR18 publication-title: Inter. J. Bifur. Chaos doi: 10.1142/S0218127419501955 – volume: 130 start-page: 191 year: 2019 ident: 7133_CR3 publication-title: Theor. Popul. Biol. doi: 10.1016/j.tpb.2019.07.016 – volume: 27 start-page: 609 issue: 6 year: 1989 ident: 7133_CR10 publication-title: J. Math. Biol. doi: 10.1007/BF00276947 – volume: 8 start-page: 74 year: 2014 ident: 7133_CR29 publication-title: Ecol. Complex. doi: 10.1016/j.ecocom.2013.06.002 – volume: 79 start-page: 1325 issue: 6 year: 2017 ident: 7133_CR36 publication-title: Bull. Math. Biol. doi: 10.1007/s11538-017-0287-0 – volume: 85 start-page: 105223 year: 2020 ident: 7133_CR16 publication-title: Commun. Nonlinear Sci. doi: 10.1016/j.cnsns.2020.105223 – volume: 334 start-page: 1398 issue: 6061 year: 2011 ident: 7133_CR40 publication-title: Science doi: 10.1126/science.1210908 – volume: 231 start-page: 534 issue: 2 year: 2006 ident: 7133_CR15 publication-title: J. Differ. Eq. doi: 10.1016/j.jde.2006.08.001 – volume: 73 start-page: 1179 issue: 5 year: 2016 ident: 7133_CR35 publication-title: J. Math. Biol. doi: 10.1007/s00285-016-0989-1 – volume: 36 start-page: 389 year: 1998 ident: 7133_CR17 publication-title: J. Math. Biol. doi: 10.1007/s002850050105 – volume: 66 start-page: 259 issue: 3 year: 2004 ident: 7133_CR12 publication-title: Theor. Popu. Biol. doi: 10.1016/j.tpb.2004.06.010 – volume: 171 start-page: 59 issue: 1 year: 2001 ident: 7133_CR38 publication-title: Math. Biosci. doi: 10.1016/S0025-5564(01)00049-9 – volume: 77 start-page: 1390 year: 1996 ident: 7133_CR19 publication-title: Ecology doi: 10.2307/2265536 – volume: 11 start-page: 49 year: 2016 ident: 7133_CR32 publication-title: Math. Model. Nat. Phenom. doi: 10.1051/mmnp/201611104 – volume: 216 start-page: 9 issue: 1 year: 2008 ident: 7133_CR4 publication-title: Math. Biosci. doi: 10.1016/j.mbs.2008.07.011 – volume: 131 start-page: 397 issue: 2–3 year: 2002 ident: 7133_CR39 publication-title: Appl. Math. Comp. doi: 10.1016/S0096-3003(01)00156-4 – volume: 22 start-page: 1 year: 2015 ident: 7133_CR1 publication-title: Ecol. Complex. doi: 10.1016/j.ecocom.2015.01.002 |
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| SubjectTerms | Automotive Engineering Behavior Birth rate Classical Mechanics Control Disease Dynamical Systems Endangered & extinct species Engineering Epidemiology Equilibrium Extinction Fear Hopf bifurcation Mechanical Engineering Ordinary differential equations Original Paper Population Population density Predators Stability Vibration |
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| Title | Complex dynamics in an eco-epidemiological model with the cost of anti-predator behaviors |
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