Dynamics of a Time-Delayed Lyme Disease Model with Seasonality

In this paper, we propose a time-delayed Lyme disease model incorporating the climate factors. We obtain the existence of a disease-free periodic solution under some additional conditions. Then we introduce the basic reproduction ratio $R_0$ and show that under the same set of conditions, $R_0$ serves as a threshold parameter in determining the global dynamics of the model; that is, the disease-free periodic solution is globally attractive if $R_0 1$. Numerically, we study the Lyme disease transmission in Long Point, Ontario, Canada. Our simulation results indicate that Lyme disease is endemic in this region if no further intervention is taken. We find that Lyme disease will die out in this area if we decrease the recruitment rate of larvae, which implies that we can control the disease by preventing tick eggs from hatching into larvae.