An Epidemic Model for Tick-Borne Disease with Two Delays

Abstract EN

We have considered an epidemic model of a tick-borne infection which has nonviraemic transmission in addition to the viremic transmission.

The basic reproduction number ℜ0, which is a threshold quantity for stability of equilibria, is calculated.

If ℜ0≤1, then the infection-free equilibrium is globally asymptotically stable, and this is the only equilibrium.

On the contrary, if ℜ0>1, then an infection equilibrium appears which is globally asymptotically stable, when one time delay is absent.

By applying a permanence theorem for infinite dimensional systems, we obtain that the disease is always present when ℜ0>1.