Mathematical Modeling on the Effects of Vaccination and Non-Pharmaceutical Interventions on Covid-19 Control Dynamics - Muli, Francis Musili (JOOUST, 2024)
COVID-19 is undoubtedly the most dangerous and highly contagious dis- ease in this century. Intensive researches have and are being done to un- earth effective vaccines to deal with future pandemics. In this research, we developed deterministic models for COVID-19 driven by asymptomatic and symptomatic individuals taking into consideration the indispensable role of vaccination in combating disease transmission. Two models were developed, the effective and ineffective vaccine models. The impact of isolating the symptomatic individuals and waning of both natural and vaccine induced immunity for recovered and vaccinated persons respec- tively were explored. Such considerations were not reconnoitred in the existing literature. The dissection of the proposed models was conferred in terms of the associated reproduction number R0, which is determined by utilizing the next-generation matrix (NGM) approach and forms the basis upon which the models’ stability analysis are established. The anal- ysis shows that COVID-19 free equilibrium (CFE) is locally asymptoti- cally stable for R0 < 1 and unstable if R0 > 1. The local stability of endemic equilibrium was explored using center manifold theorem where the method utilized by Castilo-Chavez and Song was implemented in or- der to ascertain the prerequisite for the existence of backward bifurcation. For the effective vaccine model, the recovered people’s rate of reinfection determined the direction of bifurcation while for the ineffective vaccine, backward bifurcation was driven by the vaccine efficacy. The models’ find- ings demonstrated that raising the rate at which asymptomatic persons are identified and treated significantly reduces COVID-19 transmission in the community. The results also revealed that increased administration levels of vaccine and strict adherence to isolation for the symptomatic individuals would curtail COVID-19 infections from burgeoning to catas- trophic levels that would overrun the capacity of health care support system.
Keywords: Mathematical Modeling; Vaccination; Covid-19