Modeling the variable transmission rate and various discharges on the spread of Malaria

Abstract

<abstract><p>Natural and household discharges are the natural breeding grounds of various mosquito species, including female <italic>Anopheles</italic> mosquitoes, which transmit the <italic>Plasmodium</italic> parasite, causing the spread of the life-threatening disease malaria. Apart from that, population migrations also have a substantial impact on malaria transmission, claiming about half a million lives every year around the world. To assess the effects of the cumulative density of households and other natural discharges, and emigration-dependent interaction rates on the dissemination of the vector-borne infectious disease malaria, we propose and analyze a non-linear mathematical model. The model comprises five dependent variables, namely, the density of the susceptible human population, the density of the infective human population, the density of the susceptible female <italic>Anopheles</italic> mosquito population, the density of the infective mosquito population and cumulative density of household and other natural discharges. In the model, the density of the mosquito population is supposed to follow logistic growth, whose intrinsic growth rate is a linear function of the cumulative density of household and other natural discharges. The nonlinear model is analyzed by using the stability theory of differential equations, numerical simulations and sensitivity analysis. The analysis shows that an increase in non-emigrating population causes increased incidence of malaria. It is also found that an increase in household and other natural discharges accelerates the occurrence of malaria. A basic differential sensitivity analysis is carried out to assess the sensitivity of model solutions with respect to key parameters. The model's numerical simulations demonstrate the analytical findings.</p></abstract>