Effects of allochthonous inputs in the control of infectious disease of prey. (June 2015)

• Record Type: Journal Article
• Authors: Sahoo, Banshidhar; Poria, Swarup
• Is Part Of: Chaos, solitons and fractals. Volume 75(2015)
• Page Start: 1
• Page End: 19
• Publication Date: 2015-06
• Subjects: Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2015.02.002
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Infected predator–prey model with allochthonous inputs is proposed. Stability and persistence conditions are derived. Bifurcation is determined with respect to allochthonous inputs. Results show that system can not be disease free without allochthonous inputs. Hopf and its continuation bifurcation is analysed numerically. Abstract: Allochthonous inputs are important sources of productivity in many food webs and their influences on food chain model demand further investigations. In this paper, assuming the existence of allochthonous inputs for intermediate predator, a food chain model is formulated with disease in the prey. The stability and persistence conditions of the equilibrium points are determined. Extinction criterion for infected prey population is obtained. It is shown that suitable amount of allochthonous inputs to intermediate predator can control infectious disease of prey population, provided initial intermediate predator population is above a critical value. This critical intermediate population size increases monotonically with the increase of infection rate. It is also shown that control of infectious disease of prey is possible in some cases of seasonally varying contact rate. Dynamical behaviours of the model are investigated numerically through one and two parameter bifurcation analysis using MATCONT 2.5.1 package. The occurrence of Hopf and its continuation curves are noted with the variation of infection rate and allochthonous food availability. The continuation curves of limit point cycle and Neimark Sacker bifurcation are drawn by varying the rate of infection and allochthonous inputs. This study introduces a novel natural non-toxic method for controlling infectious disease of prey in a food chain model.