International Journal of Nonlinear Analysis and Applications

The dynamics and analysis of an SIS disease of a stage-structured prey-predator model with a prey refuge

Document Type : Research Paper

Authors

1 Department of Control and Systems Engineering, University of Technology, Iraq

2 Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

Abstract

In this paper, the dynamical behaviour of an {epidemiological system} has been investigated. A stage-structured prey-predator model includes harvest and refuge for only prey, the disease of type (SIS) is just in the immature of the prey and the disease is spread by contact and by external source has been studied. The transmission of infectious diseases in the prey populations has been described by the linear type. While Lotka-Volterra functional response is used to describe the predation process of the whole prey population. This model has been represented by a set of nonlinear differential equations. The solution's existence, uniqueness and boundedness have been studied. "The local and global stability conditions of all the equilibrium points" have been confirmed. As a final point, numerical simulation has been used to study the global dynamics of the model.

Keywords

[1] Z. Kh. Alabacy and A.A. Majeed, The pear effect on a food chain prey-predator model incorporating a prey refuge and harvesting, IOP Conf. Ser. 1804 (2021) 012077.
[2] E. Bellier, B.-E. Sæther and S. Engen, Sustainable strategies for harvesting predators and prey in a fluctuating environment, Eco. Model. 440 (2021) 109350.
[3] M.-G. Cojocaru, T. Migo and A. Jaber, Controlling infection in predator-prey systems with transmission dynamics, Infect. Disease Model. 5 (2020) 1–11.
[4] U. Das, T.K. Kar and U.K. Pahari, Global dynamics of an exploited prey-predator model with constant prey refuge, Int. Scholar. Res. Notices 2013 (2013) Article ID 637640.
[5] B. Dubey and A. Kumar, Dynamics of prey-predator model with stage structure in prey including maturation and gestation delays, Nonlinear Dyn. 96 (2019) 2653–2679.
[6] A.J. Kadhim and A.A. Majeed, The impact of toxicant on the food chain ecological model, AIP Conf. Proc. 2292 (2020).
7] E.M. Kafi and A.A. Majeed, The dynamics and analysis of stage-structured predator-prey model involving disease and refuge in prey population, IOP Conference Ser. 1530 (2020) 012036.
[8] M.A. Lafta and A.A. Majeed, The food web prey-predator model with toxin, AIP Conf. Proc. 2292 (2020) 030015.
[9] Q. Liu, T. Hayat, A. Alsaedi and B. Ahmad, Dynamical behavior of a stochastic predator-prey model with stage structure for prey, Stoch. Anal. Appl. 38 (2020) 647–667.
[10] A. A. Majeed and I.I Shawka, The dynamics of an eco-epidemiological model with (SI), (SIS) epidemic disease in prey, Gen. Math. Notes 34 (2016) 52–74.
[11] A.A. Majeed, Refuge and age structures impact on the bifurcation analysis of an ecological model, J. Southwest Jiaotong Univer. 55 (2020).
[12] A.A. Majeed, The dynamics and analysis of stage-structured predator-prey model with prey refuge and harvesting involving disease in prey population, Commun. Math. Appl. 10 (2019) 337–359.
[13] A.A. Majeed and M.H. Ismaeel, The dynamical behavior of stage structured prey-predator model in the harvesting and toxin presence, J. Southwest Jiaotong Univer. 54(6) (2019) 1–8.
[14] A.A. Majeed, The dynamics of prey-predator model with prey refuge and stage structures in both populations, Sci. Int. Lahore 30 (2018) 461–470.
[15] W. Mbava, J.Y.T. Mugisha and J.W. Gonsalves, Prey, predator and super-predator model with disease in the super-predator, Appl. Math. Comput. 297 (2016) 92–114.
[16] A. Mcnabb, Comparison theorems for differential equations, J. Math. Anal. Appl. 119 (1986) 417–428.
[17] S. G. Mortoja, P. Panja and Sh. K. Mondal, Dynamics of a predator-prey model with stage-structure on both species and anti-predator behavior, Inf. Medic. Unlock. 10 (2018) 50–57.
[18] A. N. Mustafa and S. F. Amin, A harvested modified Leslie-Gower predator-prey model with SIS-disease in predator and prey refuge, J. Univer. Duhok 22 (2019) 174–184.
[19] A. Singh and P. Malik, Bifurcations in a modified Leslie–Gower predator–prey discrete model with Michaelis–Menten prey harvesting, J. Appl. Math. Comput. 67 (2021) 143-–174.
[20] A. L. Firdiansyah, Effect of prey refuge and harvesting on dynamics of eco-epidemiological model with holling type III, Jambura J. Math. 3(1) (2021) 16–25.
[21] A. Wikan and Q. Kristensen, Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest, J. Appl. Math. Comput. 67 (2021) 455—479.
[22] S.A. Wuhaib and B.A. Yaseen, Model with harvesting in food chain model, Tikrit J. Pure Sci. 25 (2020) 108–117.
[23] X. Yu, Zh. Zhu, L. Lai and F. Chen, Stability and bifurcation analysis in a single-species stage structure system with Michaelis–Menten-type harvesting, Adv. Diff. Equ. 2020 (2020) 238.
[24] H. Zhang, et al., Impact of the fear effect in a prey-predator model incorporating a prey refuge, Appl. Math. Comput. 356 (2019) 328–337.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 901-919
  • Receive Date: 03 March 2021
  • Revise Date: 05 May 2021
  • Accept Date: 20 May 2021