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Insect–pathogen model; bistable system; bifurcation.

We consider a model for insect–pathogen interaction where the insect population is divided into two groups, one group susceptible to disease and other resistant to disease. An individual born susceptible to or resistant to disease depends on the local population levels at the start of each generation. Here we consider density-dependent models of transmission because we characterize diseases that spread through environmental propagules or through random contact among individuals. We consider the case where the fraction of resistant individuals increases as the total population increases. White and Wilson (Theor. Popul. Biol. 56, 163 (1999)) have reported the results of density-dependent monotonic increase of resistance class by choosing a particular type of function. In this paper, we have chosen a class of monotonic density-dependent resistance functions and studied their effects on insect–pathogen dynamics. In particular, we have investigated the effects of different types of monotonic density-dependent resistance on the bistable nature of the model. Numerical simulation results are presented and interpreted.

Nayana Mukherjee¹ Swarup Poria¹

1. Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata 700 009, India

Published

July 2015

Manuscript received

6 May 2014

Accepted

24 July 2014

Early published

27 February 2015