A discrete-time rodent-hantavirus model structured by infection and developmental stages

Abstract

Hantaviruses are a group of viruses that infect wild rodents without causing any apparent illness or disease. New discrete-time models for the spread of hantavirus in a rodent population are formulated and analyzed. The models are structured by the stages of the infection, the stages of development, and the sex of the rodent. The basic reproduction number $\mathcal{R}_0$ is computed for the deterministic model and a condition is given for a simplified model with males only to be permanent. A stochastic model is also formulated. Numerical simulations illustrate the differences between the deterministic and stochastic models and the dynamics in the male and female rodents. It is shown, in the numerical examples, that a transcritical bifurcation occurs at $\mathcal{R}_0 = 1$ and a unique enzootic equilibrium exists when $\mathcal{R}_0 \gt 1$. The sensitivity of the equilibrium values to changes in the parameters is also investigated.