Abstract:
In this study, a novel deterministic mathematical model for the transmission
and control of malaria is formulated. The main innovation in the model is
that, in addition to the natural death rate of the vector (mosquito) population, a
proportion of the prevention effort also contributes to a reduction of the vector
population. The model assumed that a proportion ca; 0 c 1 of the prevention
effort a contributes to the death rate of the vector population. The study showed
that there exists a domain where the model is epidemiologically and mathematically
well-posed. The study showed that the model has a unique disease
free and an endemic equilibrium points. It was established that the disease free
equilibrium is locally and globally asymptotically stable when R0 < 1 and the
endemic equilibrium is locally and globally asymptotically stable when R0 > 1:
Parameters of the model were estimated from monthly confirmed malaria cases
obtained from the Central Region of Ghana. A sensitivity analysis was carried
out to determine the effects of each parameter on the basic reproduction number,
R0: The result from the sensitivity analysis showed that the two most sensitive
parameters in the reduction of R0 are prevention and treatment. Based on the
result from the sensitivity analysis, numerical simulations were performed using
various combinations of treatment and prevention to determine an optimal
combination that reduces the incidence rate fastest. The result of the simulations
showed that, with about 40% of effective prevention coupled with about 40% of
treatment, will considerably reduce both the infected human and vector populations.
The higher the prevention effort, the higher the reduction in the infected
vector population. If the prevention efforts are implemented by all contiguous
communities in the region, acting in concert, then a marked reduction should
be seen in the infected vector population leading to a complete eradication of
malaria in the region, by implication, through out Ghana.
