| The models considered for the spread of an infectious disease in a population are of SIS or SIRS type with population size dependent incidence. The varying population size is described by a differential equation which includes disease-related deaths, population size dependent birth rate and death rate functions, and, in two models, constant recruitment. Disease-reduced reproduction and vertical transmission are included in the SIS models. Thresholds, stability, host survival, the persistence of the disease, and the limitation of the host population by the persistence of the disease are determined for each model. The combination of persistence of the infectious disease and disease-related deaths can lead to a new equilibrium population size below the carrying capacity and can even cause the population to become extinct. |
