Abstract:
Malaria is a deadly vector-borne infectious disease with high prevalence in the world’s endemic tropical
and subtropical regions. Differences in individuals’ disease susceptibility may lead to their differentiation of
susceptibility to infection. We formulate a mathematical model for malaria transmission dynamics that accounts
for the host’s differential susceptibility, where partial immunity is acquired after infection. As customary, the
explicit formula for the basic reproduction number is derived and used to determine the local stability of
the model’s equilibria. An analysis of a special case with two susceptible classes shows that the model could
have two endemic equilibria when the disease threshold parameter is less than unity. Numerical simulations
are provided for a differential susceptibility when individuals are re-infected seven times after the initial
infection. Graphical representations show that the transient transmission dynamics of the infected components
are indistinguishable when there is no inflow into the susceptible classes. When there is an inflow into the
various susceptible classes, the graphs of the infected component of the model are fundamentally different,
showing that individuals who have been infected multiple times tend to be less infected over time. Knowledge
of the inflow rate and the infection reduction rate due to prior infection in each class could be key drivers to
mitigate the burden of malaria in a community.
