Effect of fast migration on prey disease in a patchy system

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Tanmay Chowdhury

Abstract

The effect of predator migration in the predator-prey system with disease in the prey population remains untouched. In this article, I have considered the individual-level migration of susceptible prey, infected prey, and predators between two different patches. I construct a couple of ODE models taking two different time scales. I consider that the individual migration of the species is faster than their demographic changes like birth, death, disease transmission, and interaction with predators. First I have study the model taking a large class of density-dependent migration rates. It has been proved that the fast equilibrium point is unique and asymptotically stable. Then I aggregate the model taking the advantage of two different time scales and construct a SIP model. The model has been investigated both analytically and numerically considering some particular type of density-dependent migrations. The theoretical study of the model includes evaluation of equilibrium points, local stability, and basic reproduction numbers in different situations. I found numerically the sensitivity of basic reproduction number with respect to migration ratios and the Switching of equilibrium points due to predator migration.

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