A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics

Area of Science:

• Epidemiological modeling
• Mathematical biology
• Computational epidemiology

Background:

• Mathematical models are crucial for predicting COVID-19 pandemic spread.
• Existing models like SIR provide a foundation for understanding disease dynamics.
• Accurate predictions require incorporating factors like vaccination and varying contact rates.

Purpose of the Study:

• To develop and analyze an extended Susceptible-Vaccinated-Infected-Critical-Deceased-Recovered (SVICDR) model.
• To investigate the impact of parameter variations on predicted COVID-19 incidence rates.
• To apply the model to recent pandemic data from Germany.

Main Methods:

• The SVICDR model is based on the Susceptible-Infectious-Recovered (SIR) framework using ordinary differential equations (ODEs).
• A novel non-standard finite difference (NSFD) scheme was designed for accurate numerical solutions of the ODE system.
• The model incorporates an exponentially increasing vaccination rate and trigonometric functions for contact and quarantine rates.

Main Results:

• The study demonstrates how modifications in model parameters influence the predicted incidence rate of COVID-19.
• The developed NSFD scheme ensures the positivity of solutions and correct asymptotic behavior, crucial for reliable predictions.
• Analysis using recent German data provides insights into pandemic dynamics under specific vaccination and control strategies.

Conclusions:

• The SVICDR model offers a robust framework for predicting regional pandemic developments.
• Parameter sensitivity analysis is vital for refining epidemiological forecasts.
• The NSFD scheme provides a stable and accurate numerical method for complex compartmental models.