Reaction-diffusion predator-prey-parasite system and spatiotemporal complexity

Bhaskar Chakraborty, Santu Ghorai and Nandadulal Bairagi

Applied Mathematics and Computation, 2020, vol. 386, issue C

Abstract: This paper deals with the spatial pattern formation in a diffusive predator-prey-parasite (PPP) model, where predator feeds on infected prey following type II response function and infection spreads among prey species through horizontal transmission. The study is accomplished with respect to an ecological parameter that quantifies the reproductive gain of predator and two epidemiological parameters which measure the force of infection and virulence of the disease. We show analytically that the interior equilibrium loses its stability through Hopf bifurcation in the absence of diffusion if the reproductive gain of predator crosses some threshold value. In case of diffusive system, it is shown that the interior equilibrium, which is otherwise stable, may lose its stability due to diffusion. Criteria for the occurrence of various types of instability, like Turing, Hopf-Turing and pure Hopf, associated with the PPP model are presented with illustrations. Our simulation results reveal that this diffusion-driven instability creates various spatio-temporal patterns, like spot, stripe, mixture of spots & stripes and spiral patterns, depending upon the values of ecological and diffusion parameters. Turing instability and the corresponding patterns are also observed with the variation of two epidemiological parameters. Interestingly, the epidemiological parameters that measure the infection rate and virulence of the disease show opposite patterns with their increasing values.

Keywords: Eco-epidemic model; Diffusion; Stability; Hopf-bifurcation; Turing instability; Pattern formation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304768

DOI: 10.1016/j.amc.2020.125518

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