Local Stability Analysis of Host-Vector Malaria Disease Model

Abstract

Many infectious diseases including malaria are preventable, yet it still
poses a threat and thus remains endemic in many communities due to
lack of appropriate, sufficient and timely control policies. Strategies for
controlling the spread of infectious disease include a reduction in both
infected populations via treatment and a possible reduction in the
susceptible population through vaccination or sensitization. In this paper,
we gleaned on some existing model and thus carry out a modification by
incorporating a vector reduction parameter as a new control strategy. We
determine the basic reproduction number of the modified model and also
investigated the existence and stability of the disease-free equilibrium
(DFE) points. We showed that the disease free equilibrium state is locally
asymptotically stable if
 1 Ro
and unstable if otherwise. This shows
that if
 1 Ro
, malaria can be controlled in the population. Finally,
numerical simulations of the model carried out using the fourth-order
Runge-Kutta numerical scheme in Matlab shows that malaria can be
eliminated in the shortest possible time