Modelling the effects of temperature variations on the dynamics of malaria.

We formulated a deterministic mathematical model to study the effects of temperature change on malaria dynamics. The model involves human host and mosquito vector sub-models. It incorporates temperature variation parameters for investigation of temperature dependent progression of infection to both human and mosquitoes. Qualitative analysis was carried out to determine the reproduction number necessary for malaria control in the community. The model equilibria are determined for disease-free equilibrium, which is locally asymptotically stable when the R0 < 1. The malaria models usually exhibits the occurrence of backward bifurcation showing a coexistence between a stable disease-free equilibrium and stable endemic equilibrium for some interval less than Ro=1, but in this study the model exhibits the forward bifurcation. Simulation results indicate that the temperature variations has higher inspect on malaria dynamics in warm areas than in cold that is, in warm areas mosquito population increases, biting rate and infection. Numerical simulations show a for-Yard bifurcation which gives an alert on understanding the endemicity of malaria in regions with temperature which allow the sufficient implementation of suitable prevention methods. More importantly, the prediction of extraordinary malaria outbreaks will allows the recruitment of emergency facilities before transmission becomes widespread.