Modeling the effects of multi-intervention campaigns for the malaria epidemic in Malawi

We develop a basic deterministic malaria model with two latent periods in the nonconstant host-vector populations, and formulate the model with intervention strategies by adding the protected and treated classes in order to assess the potential impact of protection and treatment strategies the transmission dynamics of malaria. The models are analysed qualitatively to determine criteria for control of a malaria epidemic, and are used to compute the basic reproduction and effective reproduction numbers necessary for country-wide control of malaria. The equilibria of models are determined. In addition to having a disease-free equilibrium, which is locally asymptotically stable when the R0 < 1, the basic malaria model exhibits the phenomenon of backward where a stable disease-free equilibrium coexists with a stable endemic equilibrium for a certain range of associated reproduction number less than one. Furthermore, the malaria model with intervention strategies indicates that it exhibits a forward bifurcation, in which in the absence of a low-level unstable equilibrium when the effective reproduction number Re < 1, a stable equilibrium bifurcating from the disease-free equilibrium when Re > 1, arise naturally when the disease does not invade when Re = 1. Numerical results indicate the effect of the two controls (protection and treatment) in lowering exposed and infected members of each of the populations. The result also highlights the effects of some model parameters, the infection rate and biting rate. Among the interesting dynamical behaviours of the basic malaria model, numerical simulations show a backward bifurcation which gives a challenge to the designing of the effective control measures.