Power-series solution of compartmental epidemiological models

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Science

Background:

• Compartmental epidemiological models are crucial for understanding disease spread.
• Solving the nonlinear differential equations governing these models can be challenging.
• Previous applications include analysis of the COVID-19 pandemic.

Purpose of the Study:

• To present power-series solutions as an alternative method for solving compartmental epidemiological models.
• To demonstrate the applicability of this methodology using SIR and SAIRP models.
• To validate the accuracy of the proposed approach through numerical experiments.

Main Methods:

• Utilizing power-series expansions to find solutions for systems of nonlinear differential equations.
• Applying the methodology to a standard SIR (Susceptible-Infectious-Recovered) model.
• Extending the analysis to a more complex SAIRP (Susceptible-Asymptomatic-Infectious-Recovered-Positive) model.

Main Results:

• The power-series method provides accurate solutions for the considered epidemiological models.
• The approach effectively handles the nonlinear dynamics inherent in disease transmission.
• Numerical experiments confirm the reliability and precision of the power-series solutions.

Conclusions:

• Power-series solutions offer a viable and accurate alternative for analyzing compartmental epidemiological models.
• This methodology can be applied to various models, including those relevant to real-world pandemics.
• The study validates a new computational tool for epidemiological research.