A malaria model with partial immunity in humans - Jia Li (Mathematical Biosciences and Engineering)
In this paper, we formulate a mathematical model for malaria transmission thatincludes incubation periods for both infected human hosts and mosquitoes. Weassume humans gain partial immunity after infection and divide the infected humanpopulation into subgroups based on their infection history. We derive an explicitformula for the reproductive number of infection, $R_0$, to determine thresholdconditions whether the disease spreads or dies out. We show that there exists anendemic equilibrium if $R_0>1$. Using an numerical example, we demonstrate thatmodels having the same reproductive number but different numbers of progressionstages can exhibit different transient transmission dynamics.