Non-linear transmission rates and the dynamics of infectious disease

This study considers how non-linearities in the transmission of microparasitic infections affect the population dynamics of host-parasite systems in which the disease is potentially lethal to the host. Non-linearities can either lead to a locally stable or unstable host-parasite equilibrium point, depending on the respective contributions of healthy and infected hosts to the functional form of the transmission rate. Analysis of the non-linear transmission model results in a revealing pair of local stability criteria. Specifically, stability requires sufficient total levels of intrinsic growth of the host population and total levels of density-dependent transmission. The most stable systems occur when increases in the density of healthy hosts result in increases in transmission efficiency, and increases in the number of infected hosts result in small decreases in transmission efficiency. These appear to be very reasonable relationships for directly transmitted microparasites.