Application of control and optimal treatment for predator-prey model†

Iranian Journal of Numerical Analysis and Optimization

مقاله 10، دوره 10، شماره 1 - شماره پیاپی 17، تیر 2020، صفحه 157-176   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v10i1.84901

نویسندگان

M.H. Rahmani Doust^* ؛ M. Shirazian؛ M. Shamsabadi

Department of Mathematics, Faculty of Sciences, University of Neyshabur, Neyshabur, Iran.

چکیده

Mathematical ecology and mathematical epidemiology are major fields in both biology and applied mathematics. In the present paper, a fourdimensional eco-epidemiological model with infection in both prey and preda tor populations is studied. It consists of susceptible prey, infected prey, susceptible predator, and infected predator. The functional response is assumed to be of Lotka–Volterra type. The behavior of the system such as the existence, boundedness, and stability for solutions and equilibria are studied and also the basic reproduction number for the proposed model is computed. Moreover, a related control model and optimal treatment for the control model are presented. Finally, to verify the analytical discussion, a numerical simulation is carried out.

کلیدواژه‌ها

Predator-prey؛ optimal control؛ Stability؛ Infected model

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