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In this study, a basic mathematical model for the in-human host and in-mosquito dynamics
of malaria parasite is formulated. A positive invariant region of the model was established,
and a basic reproduction number 7vo, of the model was computed. Conditions for existence
and stability of two equilibrium points: malaria free equilibrium (MFE) and malaria infection
equilibrium (MIE) were established.
The impacts of model parameters on control of malaria infection were assessed through the
sensitivity analysis of TZ q . Despite having lower sensitivity index compared to death rate of
merozoites. and death rate of schizonts have greater impact on malaria control than that of
merozoites.
The model was extended to incorporate the effect of immune responses using nonlinear bounded
Michaelis- Menten-Monod functions to describe how immune responses interact with infected
cells and parasites. Our results revealed that immunity has significant influence on reducing
malaria infection at erythrocytic and sporogonic stages, but not at exo-erythrocytic stage.
We further extended the model to incorporate the antimalarial drug therapy, where four thera
peutic classes of antimalarial drugs in various stages of entire life cycle of malaria parasite are
included. In contrast to the immunity whose effect reduces infections on only two stages, drug
therapy has the effect of reducing infection on all stages of the life cycle. Although its compo
nents do not appear in the expression of reproduction number, tissue schizonticidal drugs reveal
a substantial effect on reducing the infection at each stage of malaria life cycle.
This study suggests that a combination therapy with all four classes of antimalaria! drugs
should be developed because of its prolific effect on controlling malaria, and for such case,
an artemisinin derivatives-primaquine combination therapy is proposed. |
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