Spatiotemporal dynamics of insect pest population under viral infection

The interrelationship between pathogen infection and host mobility is of great importance for successful spread of disease in spatial pest population. As spread of infection depends on horizontal transmission of pathogen, there are numerous factors like susceptibility, latent period, host movement that influence overall effectiveness of the control policy. Initiation of new infection cycle depends on density of infected inoculum in the site. So, spatial movement of infected hosts during the course of infection influence the dynamics. Also, infected individuals are more vulnerable to predators and hence production of virus particles in the site depends on predation to some extent. We derive a four dimensional delayed reaction-diffusion model in one spatial dimension and compute the minimum travelling speed of transmission of infection. We show that the minimum speed is sensitive to several parameters of the system. For example, the minimum speed decreases only with increase in delay in lysis process, but otherwise it increases with increase in force of infection, diffusivity of infectives or per capita virus production. A concluding discussion with numerical simulation is presented in the end.