Using the SVIRS model to understand the prevention strategy for influenza with vaccination

Abstract

Influenza is an infectious disease that can threaten the lives of people at high risk of complications. As vaccines are expected to strongly aid the prevention of diseases such as influenza and COVID-19, this research discusses how a modification of the well-known Susceptible-Vaccinated-Infected-Recovered-Susceptible (SVIRS) model can help prevent these diseases. This study involves employing a combination of vaccination and social distancing as a means of preventing these diseases. The SVIRS model divides the human population into four subpopulations:, those susceptible to influenza, vaccinated, infected, and recovered from influenza. Subpopulations of people who have been given the vaccine are also assumed to be susceptible to influenza, owing to the imperfect effectiveness of the vaccine. Also, since immunity to the disease is not life-long, there is a possibility that recovered individuals may get re-infected. Analytical studies of the nondimensionalization process and the existence and stability of the equilibrium points were carried out on the model, using the bifurcation analysis. Finally, a few numerical simulations were carried out using several scenarios of vaccination and social distancing strategies. Our model indicated the possibility of backward bifurcation at ℛ0 = 1. Based on the analytical studies, ℛ0 gave an insight to determine the best strategy that can be used to prevent the spread of influenza among the population.