Using seir-sei mathematical model to illustrate the dynamics of malaria transmission in Rwanda

Abstract

Malaria showcased to be a predominant root cause of mortality in many parts of the world in general and Africa in particular. As far as Rwanda is concerned, malaria is a serious issue in a number of regions and its incidence is found to be highly variable. This explains why researchers are still working on different intervention strategies meant to alleviate it. In this research, our work consisted in studying the dynamics of malaria transmission in Rwanda using the SEIR-SEI mathematical model. The formulation and analysis of the malaria transmission model dynamics is discussed. The impact of applying nonlinear forces of infection in the control form is also presented. The optimal control problems for malaria model found the control parameters which minimize the malaria contamination in Rwanda to prevent the prevalence of infection such as reducing of exposed and infected populations, then after, comes the mosquito population. The method of next generation matrix approach helped to get the basic reproduction number R0. The presence of the endemic equilibrium was also identified under condition. The real data of malaria in Rwanda context were used to identify the parameters of our malaria model and the calculation were done using MaTlaB. The numerical simulation showed that the number of exposed and infected people and mosquito population are decreased due to the control strategies. The findings show that the existence of an optimal control problem for the most effective intervention strategy in reduction of infected population and increasing the susceptible and recover human is the combination of two or more controls. Finally, this work found out that the transmission of malaria with special to Rwanda can be minimized by using the combination of controls like Insecticide Treated bed Nets (ITNs), Indoor Residual Spray (IRS) and Artemisinin based Combination Therapies (ACTs). This work points out some interesting directions for the future research such as mathematical model that focus many factors influencing the spread of malaria in Rwanda, mathematical model with considering four or more control measures strategies of malaria in Rwanda.