A Modified SIVR Mathematical Model of Covid-19 Post-vaccination Stability Analysis in Kenya

In this paper, the study focused on carrying out a stability analysis on a modified SIR model for the COVID-19 pandemic for the period after vaccination in Kenya. The purpose of the work was to show that whereas the rate and the extent of disease spread amongst the Kenyan people was not as wide spread as happened in other parts of the world, it was necessary for government and policy makers to roll out a robust civic education to convince the majority of the Kenyan population to embrace vaccination as a major containment measure in curbing the spread of COVID-19 and other infectious diseases since the study revealed that the infections drastically reduced to near zero after vaccination except for a few isolated cases that were and still continue to exhibit mild symptoms to none at all. This was attributed to the development of the vaccine which upon a massive campaign by the Kenyan government, led into a significant portion of the population being vaccinated. It is believed this vaccination drive enhanced herd immunity amongst the population. This development has had a significant effect in the control of more recent COVID-19 variants like JN-1 that have remained largely mild and undetected in the country. Both local and global post vaccination stabilities were analyzed for the system using the Lyapunov function. The main objective of the study was therefore to carry out a post vaccination stability analysis by estimating key parameters such as the basic reproduction number, ( R0) and herd immunity threshold (HIT) for infectious diseases by fitting data into the model to enable predictions of future dynamics of the disease. The study used the Next Generation matrix and the least square method besides the Python software to solve generated differential equations of the model for and HIT parameters. Results obtained showed that, there was a significant reduction in infections due to enhanced herd immunity attributed largely to the roll out of vaccination.