Effects of complexity and seasonality on backward bifurcation in vector–host models

We study implications of complexity and seasonality in vector–host epidemiological models exhibiting backward bifurcation. Vector–host diseases represent complex infection systems that can vary in the transmission processes and population stages involved in disease progression. Seasonal fluctuations in external forcing factors can also interact in a complex way with internal host factors to govern the transmission dynamics. In backward bifurcation, the insufficiency of R(0) < 1 for predicting the stability of the disease-free equilibrium (DFE) state arises due to existence of bistability (coexisting DFE and endemic equilibria) for a range of R(0) values below one. Here we report that this region of bistability decreases with increasing complexity of vector-borne disease transmission as well as with increasing seasonality strength. The decreases in the bistability region are accompanied by a reduced force of infection acting on primary hosts. As a consequence, we show counterintuitively that a more complex vector-borne disease may be easier to control in settings of high seasonality.