Mathematical Models for Dynamics and Control Strategies for Rotavious Disease

Abstract

This dissertation investigates a mathematical model for the dynamics and control strategies for rotavirusdisease,first,tostudytheeffectoftreatmentandvaccinationcontrolsonthedynamics of the disease, stability analysis of disease-free-equilibrium point (DFEP) and endemic equilibrium point (EEP) were performed. The computational results show that DFEP is globally asymptotically stable if the basic reproduction number, R0 < 1 and unstable if R0 > 1. The EEP exits if and only if the effective reproduction number, Re > 1. Numerical simulations obtained show that treatment and vaccination can be used to fight rotavirus disease. To assess the best control strategy among vaccination, treatment and health education campaigns control measures in the dynamics of the rotavirus, we analysed the conditions for optimal control using the optimal control theory to find the optimal curve for each of the controls. Our results show that control measures have a very desirable effect for minimising the number ofinfectedindividualsaswellasmaximisingthenumberofsusceptiblesandthatmultiplecontrol strategies are more effective than a single control strategy. Furthermore, we obtained that, health education campaigns should not be implemented alone because they are less effective at the beginning if implemented alone but the combination which involves vaccination gives better results. To investigate the effect of vaccination when administered in three doses on the dynamics of the disease. Using the comparison approach the global stability of the DFEP with vaccination was computed. In case of no vaccination, a forward bifurcation exits whenever the basic reproduction number, R0 > 1. Numerical results show that vaccination reduces the degree of susceptibility and infectiousness when children are exposed to rotavirus disease. Using the pontryagin’s maximum principle to asses the impact of three dose vaccination and treatment controls, the performed simulations show that with no control, infection will disappearafter75days,withtreatmentonly,ittakes55days,withvaccinationonly,ittakesbetween i 30 to 40 days and if both measures are implemented it takes only 10 days to disappear, thus infection is wiped out in a very short period compared to when only one strategy is used.