A Delayed Vaccination Model for Rotavirus

Abstract

Rotavirus is the most common cause of severe gastroenteritis infection in infants and young children, occurring even with very high standard of hygiene. The disease spreads by contact with infected faeces and might also be transmitted through faecally-contaminated: food, water and respiratory droplets. Rota teq and Rotarix are the two licensed oral vaccine intervention for rotavirus. However, it takes time for the development of vaccineinduced immunity to complete, hence the need to investigate the impact of this time delay on the dynamics of rotavirus. The objectives of the study were: to formulate a mathematical model for rotavirus incorporating time delay in vaccination; to perform stability analysis of the model formulated and to simulate the long term effect of time delay. A mathematical model based on a system of delay differential equation for rotavirus incorporating time delay in the effects of vaccination was formulated. The disease free equilibrium has been proved to be both locally and globally stable. The endemic equilibria is proved to be locally stable whenever = 0 and undergoes a Hopf bifurcation if > 0. From the analytical and simulation results, we observe a decrease in rotavirus infection as result of using vaccine with high efficacy rates and a shorter delay time. Hence we recommend vaccine with high efficacy rates and a shorter delay time should be introduced in order to effectively control rotavirus infections. The fundings of this study can be adopted by policy makers and health practitioners in planning and allocation of resources towards vaccination strategies for control of rotavirus infection.