Mathematical Modelling of Intra and Inter Dynamics and Control of Yellow Fever in Primate and Humna Populations

Abstract

A deterministic mathematical model was formulated using non-linear ordinary differential equations to gain an insight of dynamics of yellow fever (YF) between primates, human beings and Aedes mosquito for the purpose of controlling the disease. Basic reproduction number, R0, was computed and its sensitivity analysis with respect to epidemiological parameters was performed to study the effect of model parameters to R0. Results showed that R0 is most sensitive to daily biting rate of mosquitoes, recruitment rate of vectors, probability of transmission of infection, recruitment of unvaccinated immigrants and the incubation period for both vector and humans. Thus, for the minimization of YF transmission, these parameters should closely be monitored. Stability analysis of disease-free equilibrium (DFE) and endemic equilibrium (EE) points were performed to study perseverance and conditionnecessaryfordiseaseinterruptionandcontrol. ResultsshowedthattheDFEislocally asymptotically stable if the rate of new infection from infected monkey to vector is less than unity, and is globally asymptotically stable if the rate of new infection from infected vector to human is less than unity. Lyapunov stability theory and LaSalles Invariant Principle were used to investigate stability of EE. Results show that EE is globally asymptotically stable whenever R0 > 1. To assess the impact of control measures on YF dynamics, we derived and analysed the necessary conditions for optimal control using optimal control theory. Results show that multipleoptimalcontrolstrategyisthemosteffectivetobringastabledisease-freeequilibrium compared to single and two controls. However, spray of insecticides alone was not effective without personal protection, and optimal use of personal protection alone is beneficial to minimize transmission of the infection to the community. Furthermore, cost-effectiveness analysis of the optimal control measures was considered. We used incremental cost-effectiveness ratio to investigate and compare the costs required against the health benefits achieved between two or more alternative intervention strategies that compete for the same resource. Results showed that combination of all strategies is the most cost-effective compared to others.