SIRSi-vaccine dynamical model for the Covid-19 pandemic

Area of Science:

• Epidemiology
• Mathematical Modeling
• Public Health

Background:

• The Covid-19 pandemic necessitated rapid development of control strategies.
• Understanding disease dynamics, including unreported cases and temporary immunity, is crucial for effective pandemic response.
• Vaccination and nonpharmaceutical interventions are key to managing infectious disease outbreaks.

Purpose of the Study:

• To propose and analyze a novel mathematical model (SIRSi-vaccine) for Covid-19 spread.
• To investigate the impact of vaccination rates and social isolation on disease dynamics.
• To assess strategies for mitigating the pandemic by combining vaccination and nonpharmaceutical interventions.

Main Methods:

• Development of a susceptible-infected-removed-sick model with vaccination (SIRSi-vaccine).
• Analysis of transcritical bifurcation to determine disease-free and endemic equilibria.
• Model fitting with epidemiological data from São Paulo, Brazil, including confirmed cases and isolation index.

Main Results:

• The study identified equilibrium conditions and estimated maximum confirmed cases based on model parameters.
• Bifurcation analysis revealed the interplay between vaccination rate and isolation index.
• Simulations showed potential for oscillatory behavior in susceptible populations and case counts driven by isolation index fluctuations.

Conclusions:

• Combining vaccination with social isolation requires minimal effort for disease control and ensures stable equilibria.
• The SIRSi-vaccine model offers valuable insights for policymakers on integrated prevention strategies.
• The model effectively assesses unreported infections, temporary immunity, and the impact of social distancing.