Cumulative damage for multi-type epidemics and an application to infectious diseases

Area of Science:

• Epidemiology
• Stochastic Modeling
• Biostatistics

Background:

• Epidemics cause significant population damage, with random case occurrences and severity.
• Quantifying this damage requires robust statistical frameworks.
• Existing models may not fully capture the multivariate and continuous-time nature of epidemic spread and impact.

Purpose of the Study:

• To develop a continuous-time multivariate stochastic model for assessing epidemic-induced population damage.
• To analyze the behavior of damage accumulation and stopping times related to epidemic thresholds.
• To provide statistical inference tools for epidemic parameters, including a homogeneity test.

Main Methods:

• Utilized counting processes and multivariate mark processes to model cumulative damage.
• Employed asymptotic distribution approximations for large populations.
• Developed and applied a general hypothesis test for epidemic homogeneity.

Main Results:

• The proposed model effectively assesses damage from multi-type epidemics.
• Asymptotic distributions approximate the damage process for large populations.
• A homogeneity test was successfully applied to COVID-19 data in Chile, demonstrating its utility.

Conclusions:

• The stochastic model offers a novel approach to quantifying epidemic damage.
• Statistical inference tools, particularly the homogeneity test, are valuable for epidemic analysis.
• The methodology provides insights into epidemic dynamics and control strategies.