The influence of the multiplicity of infection upon the dynamics of a crop-pest–pathogen model with defence mechanisms

To prevent pest outbreaks, growers often resort to the release of insect-pathogenic viruses rather than to the use of pesticides, which threaten human health and adversely impact the environment. One of the unfortunate consequences of this approach, however, is the onset of resistance mechanisms in pests. In this paper, we propose a model which couples the analysis of the within-pest virus dynamics and the investigation of the evolutionary response of defence mechanisms. The ecosystem consisting in the soybean crop and its major pest, the fourth instar larvae of Spodoptera litura, which is infected by Spodoptera polyhedrosis viral particles, is used as our main example. Five types of resistance mechanisms are investigated, each expressing resistance through one or more model parameters. By means of linearization, phase field analysis and numerical simulations, we illustrate and analyze the stability of the steady states of our model. Moreover, we use a graph representing the values of the function of the lifetime reproductive success of the mutant in the resident pest population at equilibrium states to find which are the best and the worst pest control strategies. Our findings show the impact of evolutionary resistance on the selection for the multiplicity of infection of the within-pest virus, in the sense that to establish the viral infection there is a threshold of the mutant trait.