An epidemic model for tick-borne disease with two delays
Summary: 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 \(\mathfrak R_0\), which is a threshold quantity for stability of equilibria, is calculated. If \(\mathfrak R_0 \leq 1\), then the infection-free equilibrium is globally asymptotically stable, and this is the only equilibrium. On the contrary, if \(\mathfrak R_0> 1\), 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 \(\mathfrak R_0>1\).
scientific article; zbMATH DE number 6950670