A Multi-Patch Epidemic Model with Periodic Demography, Direct and Indirect Transmission and Variable Maturation Rate

A deterministic epidemic model describes the propagation of Puumala hantavirus within the bank vole population of Clethrionomys glareolus. The host population is split into juvenile and adult individuals. Demographic parameters are time periodic. A further spatial structure is considered using a multi-patch model. Indirect transmission through environment is considered. Maturation and dispersion rates for juvenile individuals are adult density-dependent. Using bifurcation techniques, small periodic perturbations of constant coefficients are shown to lead to the emergence of periodic endemic states from locally asymptotically stable stationary states. Numerical simulations show that in some circumstances the virus is favored by periodical dynamics compared with constant dynamics.