Dynamic malaria models with environmental changes

In this paper, we formulate a dynamic model for the transmission of malaria in both host human and vector mosquito populations. We include incubation periods for both infected human hosts and mosquitoes. We further divide the infected human population into subgroups based on their infection history. Threshold conditions which determine whether the disease spreads in the human and vector populations or dies out are obtained. Such conditions are characterized by the reproductive number and an explicit formula for the reproductive number is derived. The reproductive number is composed of key parameters in the disease transmission and those parameters are functionals of environmental variables. Impact of environmental changes on the disease transmission is then discussed through the sensitivity of the reproductive number with respect to the environmental variable.