Modeling the Control of the Spread of Infectious Diseases with Vaccination Strategy

Infectious diseases remain a significant concern for families and society at large, causing severe impacts globally. This study addresses the spread of infectious diseases using the Susceptible-Infected-Removed-Vaccinated (SIRV) model. The model categorizes recovered individuals into two groups: those who recover through vaccination and those who recover without vaccination. Furthermore, the SIRV model is analyzed under two scenarios: with and without a “death factor.” Unlike other models, vaccination is introduced directly into the infective class. The solution and stability analysis of the model reveals that the basic reproduction number in both the disease-free and endemic states is less than one indicating that the infectious disease gradually dies out within the population. Simulation results validate the model, providing a clear illustration of how vaccination significantly reduces the disease spread and ultimately eliminates it from the population. This study demonstrates that the introduction of vaccination into populations affected by infectious diseases is a highly effective strategy for minimizing disease spread. Simulated data further corroborate the findings, offering valuable insights and reinforcing the potential of vaccination programs to curb infectious diseases.