  A deterministic multi-stage malaria model with a non-therapeutic control
measure, the use of mosquito bednet is formulated and analyzed. The model basic
reproduction number is derived, and analytical results show that the models
equilibria are locally and globally asymptotically stable when certain
threshold conditions are satisfied. Pontryagin's Maximum Principle with respect
to a time dependent constant is used to derive the necessary conditions for the
optimal usage of the Long-Lasting Insecticide-treated bednets(LLINs) to
mitigate the malaria transmission dynamics. This is accomplished by introducing
biologically admissible control and e-approximate sub-optimal control. The
results from this study could help public health planners and policy
decision-makers to design reachable and more practical malaria prevention
programs "close" to the optimal strategy.
