An almost periodic Ross–Macdonald model with structured vector population in a patchy environment
An almost periodic Ross–Macdonald model with age structure for the vector population in a patchy environment is considered. The basic reproduction ratio $$R_{0}$$ R 0 for this model is derived and a threshold-type result on its global dynamics in terms of $$R_{0}$$ R 0 is established. It is shown that the disease is uniformly persistent if $$R_{0}>1$$ R 0 > 1 , while the disease will die out if $$R_{0}<1$$ R 0 < 1 . Numerical simulations show that the biting rate greatly affects the disease transmission, and human migration sometimes could reduce the transmission risk. We further obtain a condition numerically to determine whether a control strategy on migration is necessary. Moreover, numerical results indicate that prolonging the length of maturation period of vector is beneficial to the disease control, and the threshold length of the maturation period for disease outbreak can be computed. Finally, the comparison between the almost periodic and periodic models shows that the periodic model may overestimate or underestimate the disease transmission risk.