A transmission model for a disease with some fatalities

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Modeling

Background:

• Stochastic epidemic models are crucial for understanding disease spread.
• Existing models may not fully capture outcomes with disease-induced mortality.
• The general epidemic and fatal disease models are specific instances.

Purpose of the Study:

• To develop a flexible stochastic epidemic model incorporating disease-related deaths.
• To analyze the probability distribution of epidemic final size.
• To derive and evaluate an efficient parameter estimator.

Main Methods:

• Formulation of a stochastic epidemic model with mortality.
• Derivation of iterative equations for final size probability distribution.
• Development of a computationally efficient parameter estimator.

Main Results:

• The model encompasses general epidemic and fatal disease scenarios.
• The fatal disease model exhibits dichotomous outcomes in large populations (near-total infection or minimal spread).
• The derived estimator demonstrates good efficiency compared to the maximum likelihood estimator.

Conclusions:

• The proposed model offers a more comprehensive framework for epidemic analysis, especially with mortality.
• The distinct behavior of the fatal disease model has significant implications for public health interventions.
• The efficient estimator simplifies parameter estimation in complex epidemic models.