Stationary distribution and global stability of stochastic predator-prey model with disease in prey population

References

• C. Arora and V. Kumar, Dynamics of one-prey and two-predator system highlighting the significance of additional food for predators with Beddington-DeAngelis functional response, Differ. Equat. Dyn. Syst. 30 (2018), pp. 411–431.
   Google Scholar
• L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, New York, 1974.
   Google Scholar
• R.M. Anderson and R.M. May, The invasion, persistence and spread of infectious diseases within animal and plant communities, Philos. Trans. R. Soc. London B 314(1167) (1986), pp. 533–570.
   PubMed Web of Science ®Google Scholar
• J.R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol. 44 (1975), pp. 331–340.
   Web of Science ®Google Scholar
• Z. Cao, W. Feng, X. Wen, and L. Zu, Stationary distribution of a stochastic predator-prey model with distributed delay and higher order perturbations, Phys. A: Statis. Mech. Its Appl. 521 (2019), pp. 467–475.
   Web of Science ®Google Scholar
• N. Dalal, D. Greenhalgh, and X. Mao, A stochastic model for internal HIV dynamics, J. Math. Anal. Appl. 341(2) (2008), pp. 1084–1101.
   Web of Science ®Google Scholar
• D.L. DeAngelis, R.A. Goldstein, and R.V. O'Neill, A model for trophic interaction, Ecology 56 (1975), pp. 881–892.
   Web of Science ®Google Scholar
• B. Du, M. Hu, and X. Lian, Dynamical behavior for a stochastic predator-prey model with HV type functional response, Bull. Malaysian Math. Sci. Soc. 40(1) (2017), pp. 487–503.
   Web of Science ®Google Scholar
• B. Dubey and R.K. Upadhyay, Persistence and extinction of one-prey and two-predators system, Nonlinear Anal.: Modell. Cont. 9(4) (2004), pp. 307–329.
   Google Scholar
• M. Fan and Y. Kuang, Dynamics of a nonautonomous predator-prey system with the Beddington–DeAngelis functional response, J. Math. Anal. Appl. 295(1) (2004), pp. 15–39.
   Web of Science ®Google Scholar
• J.M. Fryxell and P. Lundberg, Diet choice and predator-prey dynamics, Ecol. Evol. 8 (1994), pp. 407–421.
   Web of Science ®Google Scholar
• C. Gokila and M. Sambath, Analysis on stochastic predator-prey model with distributed delay, Rand. Oper. Stochast. Equat. 29(2) (2021), pp. 97–110.
   Web of Science ®Google Scholar
• C. Gokila, M. Sambath, K. Balachandran, and Y.-K. Ma, Analysis of stochastic predator-prey model with disease in the prey and Holling type II functional response, Adv. Math. Phys. 2020 (2020), pp. 1–17.
   Web of Science ®Google Scholar
• Y. Huang, W. Shi, C. Wei, and S. Zhang, A stochastic predator-prey model with Holling II increasing function in the predator, J. Biol. Dyn. 15(1) (2021), pp. 1–18.
   PubMed Web of Science ®Google Scholar
• T.W. Hwang, Global analysis of the predator-prey system with Beddington–DeAngelis functional response, J. Math. Anal. Appl. 281(1) (2003), pp. 395–401.
   Web of Science ®Google Scholar
• C. Ji and D. Jiang, Analysis of a predator-prey model with disease in the prey, Int. J. Biomath. 6(3) (2013), p. 1350012.
   Web of Science ®Google Scholar
• C. Ji, D. Jiang, and N. Shi, Analysis of a predator-prey model with modified Leslie–Gower and Holling-type II schemes with stochastic perturbation, J. Math. Anal. Appl. 359(2) (2009), pp. 482–498.
   Web of Science ®Google Scholar
• W. Kermack and A. McKendrick, Contributions to the mathematical theory of epidemics, I II, III, Bullet. Math. Biol. 53 (1991), pp. 33–55;57–87;89–118.
   PubMed Web of Science ®Google Scholar
• R. Khasminskii, Stochastic Stability of Differential Equations, Springer, Berlin, 2011.
   Google Scholar
• B.W. Kooi and E. Venturino, Ecoepidemic predator-prey model with feeding satiation, prey herd behavior and abandoned infected prey, Math. Biosci. 274 (2016), pp. 58–72.
   PubMed Web of Science ®Google Scholar
• J. Li and W. Gao, Analysis of predator-prey model with disease in prey, Appl. Math. Comput. 217 (2010), pp. 4024–4035.
   Web of Science ®Google Scholar
• X. Li and X. Mao, Population dynamical behavior of non-autonomous Lotka–Volterra competitive system with random perturbation, Discrete Continuous Dyn. Syst.-Ser. A 24(2) (2009), pp. 523–593.
   Web of Science ®Google Scholar
• S. Li and X. Wang, Analysis of a stochastic predator-prey model with disease in the predator and Beddington-DeAngelis functional response, Adv. Differ. Equat. 2015(1) (2015), pp. 1–21.
   Google Scholar
• M. Liu, C. Du, and M. Deng, Persistence and extinction of a modified Leslie–Gower Holling-type II stochastic predator-prey model with impulsive toxicant input in polluted environments, Nonlinear Anal.: Hybrid Syst. 27 (2018), pp. 177–190.
   Web of Science ®Google Scholar
• Q. Liu and D. Jiang, Stationary distribution and extinction of a stochastic predator-prey model with distributed delay, Appl. Math. Lett. 78 (2018), pp. 79–87.
   Web of Science ®Google Scholar
• Q. Liu, D. Jiang, T. Hayat, and A. Alsaedi, Stationary distribution and extinction of a stochastic predator-prey model with herd behavior, J. Franklin Inst. 355(16) (2018), pp. 8177–8193.
   Web of Science ®Google Scholar
• C. Lu, Dynamical analysis and numerical simulations on a Crowley–Martin predator-prey model in stochastic environment, Appl. Math. Comput. 413 (2022), p. 126641.
   Web of Science ®Google Scholar
• P.S. Mandal and M. Banerjee, Stochastic persistence and stationary distribution in a Holling–Tanner type prey-predator model, Phys. A: Statis. Mech. Its Appl. 391(4) (2012), pp. 1216–1233.
   Web of Science ®Google Scholar
• X. Mao, Stochastic versions of the Lassalle theorem, J. Differ. Equat. 153(1) (1999), pp. 175–195.
   Web of Science ®Google Scholar
• R.M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, 2001.
   Google Scholar
• A. Mondal, A.K. Pal, and G.P. Samanta, On the dynamics of evolutionary Leslie–Gower predator-prey eco-epidemiological model with disease in predator, Ecol. Genet. Genom. 10 (2019), p. 100034.
   Google Scholar
• D. Mukherjee, Persistence aspect of a predator-prey model with disease in the prey, Differ. Equat. Dyn. Syst. 24(2) (2016), pp. 173–188.
   Google Scholar
• M. Pitchaimani and R. Rajaji, Stochastic asymptotic stability of Nowak-May model with variable diffusion rates, Methodol. Comput. Appl. Probab. 18(3) (2016), pp. 901–910.
   Web of Science ®Google Scholar
• R. Rudnicki, Long-time behaviour of a stochastic prey-predator model, Stochast. Process. Their Appl.108(1) (2003), pp. 93–107.
   Web of Science ®Google Scholar
• M. Sambath and K. Balachandran, Bifurcation analysis of a diffusive predator-prey model with Beddington–DeAngelis response, Nonlinear Stud. 22(2) (2015), pp. 263–280.
   Google Scholar
• M. Sambath, K. Balachandran, and M. Suvinthra, Stability and Hopf bifurcation of a diffusive predator prey model with hyperbolic mortality, Complexity 21(1) (2016), pp. 34–43.
   Google Scholar
• S. Sharma and G.P. Samanta, Analysis of a two prey one predator system with disease in the first prey population, Int. J. Dyn. Cont. 3(3) (2015), pp. 210–224.
   Google Scholar
• P.D.N. Srinivasu, D.K.K. Vamsi, and V.S. Ananth, Additional food supplements as a tool for biological conservation of predator-prey systems involving type III functional response: A qualitative and quantitative investigation, J. Theor. Biol. 455 (2018), pp. 303–318.
   PubMed Web of Science ®Google Scholar
• T.V. Ton and A. Yagi, Dynamics of a stochastic predator-prey model with the Beddington–DeAngelis functional response, Commun. Stochast. Anal. 5(2) (2011), pp. 371–386.
   Google Scholar
• J.P. Tripathi, S. Abbas, and M. Thakur, Dynamical analysis of a prey-predator model with Beddington–DeAngelis type function response incorporating a prey refuge, Nonlinear Dyn. 80(1-2) (2015), pp. 177–196.
   Web of Science ®Google Scholar
• C. Qin, J. Du, and Y. Hui, Dynamical behavior of a stochastic predator-prey model with Holling-type III functional response and infectious predator, AIMS Math. 7(5) (2022), pp. 7403–7418.
   Web of Science ®Google Scholar
• R. Wu, X. Zou, and K. Wang, Asymptotic behavior of a stochastic non-autonomous predator-prey model with impulsive perturbations, Commun. Nonlinear Sci. Numerical Simul. 20(3) (2015), pp. 965–974.
   Web of Science ®Google Scholar
• Y. Zhang, S. Gao, and S. Chen, A stochastic predator-prey eco-epidemiological model with the fear effect, Appl. Math. Lett. 134 (2022), p. 108300.
   Web of Science ®Google Scholar
• Y. Zhang, S. Gao, K. Fan, and Y. Dai, On the dynamics of a stochastic ratio-dependent predator-prey model with a specific functional response, J. Appl. Math. Comput. 48(1-2) (2015), pp. 441–460.
   Google Scholar
• Q. Zhang, D. Jiang, Z. Liu, and D. O'Regan, The long-time behavior of a predator-prey model with disease in the prey by stochastic perturbation, Appl. Math. Comput. 245 (2014), pp. 305–320.
   Web of Science ®Google Scholar
• D. Zhou, M. Liu, and Z. Liu, Persistence and extinction of a stochastic predator-prey model with modified Leslie–Gower and Holling-type II schemes, Adv. Differ. Equat. 2020(1) (2020), pp. 1–15.
   PubMed Web of Science ®Google Scholar