A mathematical model for endemic malaria with variable human and mosquito populations

A deterministic differential equation model for endemic malaria involving variable human and mosquito populations is analysed. Conditions are derived for the existence of endemic and disease-free equilibria. A threshold parameter R̄0 exists and the disease can persist if and only if R̄0 exceeds 1. The disease-free equilibrium always exist and is globally stable when R̄0 is below 1. Numerical simulations show that the endemic equilibrium, when it exists, is unique and is globally stable.