Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation | Zendy

Chao Liu | Zendy; Qingling Zhang | Zendy; Jinna Li | Zendy

Open Access

Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation

Author(s) -

Chao Liu,

Qingling Zhang,

Jinna Li

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/950396

Subject(s) - pontryagin's minimum principle , mathematics , predation , maximum principle , population , overexploitation , predator , consistency (knowledge bases) , optimal control , stability (learning theory) , mathematical optimization , control theory (sociology) , mathematical economics , control (management) , ecology , economics , biology , computer science , demography , geometry , management , machine learning , sociology

We propose an ecoepidemiological prey predator model, where selective harvest effort on predator population is considered. Vaccination and taxation are introduced as control instruments, which are utilized to control number of susceptible prey population and protect predator population from overexploitation, respectively. Conditions which influence nonnegativity and boundedness of solutions are studied. Global stability analysis around disease-free equilibrium is discussed based on robust Bendixson criterion, which is theoretically beneficial to studying coexistence and interaction mechanism of population within harvested ecoepidemiological system. By using Pontryagin’s maximum principle, an optimal control strategy is derived to maximize the total discounted net economic revenue to society as well as protect prey population from infectious disease. Numerical simulations are carried out to show the consistency with theoretical analysis

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