Modelling and inference for epidemic models featuring non-linear infection pressure.

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Modeling

Background:

• The standard Susceptible-Infective-Removed (SIR) model is a cornerstone of epidemic dynamics.
• Modifications to the standard SIR model are crucial for understanding complex disease spread patterns.
• The infection rate in epidemic models significantly influences disease transmission dynamics.

Purpose of the Study:

• To analyze a modified Susceptible-Infective-Removed (SIR) stochastic epidemic model with a generalized infection rate.
• To investigate how the parameter α in the infection rate βN⁻¹X(t)Y(t)(α) alters the model's threshold behavior.
• To develop and evaluate statistical inference methods for estimating parameters in this modified SIR model using outbreak data.

Main Methods:

• Stochastic SIR epidemic modeling with a modified infection rate.
• Comparative analysis of the modified model against the standard SIR model (α=1).
• Development of statistical inference techniques for parameter estimation.

Main Results:

• The modified SIR model exhibits significantly different threshold behavior compared to the standard SIR model.
• The generalized infection rate parameter α markedly impacts epidemic dynamics.
• The study assesses the identifiability of all three model parameters from outbreak data.

Conclusions:

• The generalized infection rate in the SIR model leads to substantial deviations from standard epidemic predictions.
• Understanding these deviations is critical for accurate disease forecasting and control.
• The proposed statistical methods provide a framework for parameter estimation in modified epidemic models.