A malaria model with partial immunity in humans (Q1000278)

This paper introduces a mathematical model for malaria transmission that includes incubation periods for both infected human hosts and mosquitoes. It is assumed that humans gain partial immunity after infection and the infected human population is divided into subgroups according to their infection history. It is observed that an explicit formula regarding the reproductive number of infection, to determine threshold conditions whether the disease spreads or dies out. Also, it is shown that there exists an endemic equilibrium if the reproductive number of infection is greater than one. By using a numerical example, it is indicated that even though the models have the same reproductive number, different numbers of progression stages can exhibit different transient transmission dynamics.