Determination of the risk of malaria using different models for mosquito biting and mortality rates

Abstract

Malariais a serious and sometimes a fatal epidemic affecting nearly half of the world’s population. In this project, we analyse a non-linear deterministic model to assess the relation between rainfall, temperature, relative-humidity as climatic variables and malaria incidence. The seven equations from the compartmental model were reduced to two of which was used to derive the reproduction number as a function of the climatic variables. We analysed both the local and global stability of the disease free equilibrium points and also the local stability of the endemic equilibrium. We settled on two different biting rates and two different mortality rates so as to accommodate the different climatic variables under study. Our scope to analyse different biting and mortality rates was achieved by simultaneously substituting two models; one biting rate and one mortality rate into the reproduction number after which numerical simulations are provided to determine the correlation between climatic variables and malaria incidence. Apart from reproduction number, the other index used in the analysis of the relation between temperature and future risk of malaria is the epidemic potential which showed qualitatively that an increase or decrease in temperature will lead to a corresponding behaviour in malaria incidence. Our findings in this study confirm that indeed there is some correlation between climatic variables and the dynamics of both total and confirmed malaria incidence.