Statistical inference for unknown parameters of stochastic SIS epidemics on complete graphs

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Processes

Background:

• The susceptible-infectious-susceptible (SIS) model is a fundamental framework for studying epidemic dynamics.
• Stochastic models are crucial for capturing random fluctuations inherent in real-world disease spread.
• Parameter estimation is vital for understanding and predicting epidemic behavior.

Purpose of the Study:

• To develop consistent estimations for infection and recovery rates in a stochastic SIS model on a complete graph.
• To establish the asymptotic behavior of these estimations using central limit theorem (CLT) and moderate deviation principle (MDP).
• To demonstrate practical applications of the derived theoretical results in statistical inference.

Main Methods:

• Utilizing the theory of density-dependent Markov chains for parameter estimation.
• Analyzing the asymptotic properties of estimators as the number of vertices (n) tends to infinity.
• Applying CLT and MDP to the estimated parameters.

Main Results:

• Consistent estimators for infection and recovery rates were derived for large populations (n → ∞).
• The central limit theorem (CLT) and moderate deviation principle (MDP) were established for these estimators.
• Applications include defining hypothesis testing reject regions and constructing confidence intervals with desirable asymptotic properties.

Conclusions:

• The study provides a robust theoretical framework for parameter estimation in stochastic epidemic models.
• The established CLT and MDP facilitate reliable statistical inference for epidemic model parameters.
• The findings contribute to a deeper understanding of epidemic dynamics and forecasting through advanced mathematical methods.