Evaluating the Impact of Epidemic Control via State-Dependent Markovian Switching Modeling

2026-07-20

AI Summary

This study addresses the precise evaluation of adaptive intervention strategies on infectious disease dynamics, with a focus on their joint impact on cumulative infections and epidemic duration. To this end, it introduces—for the first time—a state-dependent Markov-switching mechanism into a finite-population stochastic SIR model, allowing transmission, recovery, and immunity parameters to adapt dynamically to the epidemic state. Exploiting the monotonicity of the susceptible count, the authors develop a hierarchical recursive algorithm that efficiently computes the joint distribution, conditional Laplace–Stieltjes transform, and mixed moments of extinction time and total infections, circumventing the need to solve large linear systems. Using weekly monkeypox incidence data from Luxembourg, combined with a Poisson observation model and maximum likelihood calibration, the study quantitatively compares fixed, delayed, vaccine-assisted, and state-dependent escalation strategies, demonstrating the latter’s marked superiority in reducing both infection burden and epidemic duration.

Abstract

We develop an exact finite-population stochastic framework for SIR epidemics evolving under Markovian switching between intervention regimes. The epidemic state is augmented by a finite phase component, allowing transmission, recovery, and direct immunity-acquisition rates to depend on the active regime. Phase-transition intensities may depend on the current epidemic state, so that policy escalation can react to the number of infectious individuals. Exploiting the monotonicity of the susceptible compartment, we derive level-wise recursions for the joint Laplace--Stieltjes transform and probability generating function of the extinction time and the number of infections generated before extinction. These recursions yield the infection-count distribution, conditional extinction-time transforms, and mixed moments linking epidemic duration and infection burden, while replacing a large global linear system with small phase-level solves. The framework is illustrated using weekly mpox incidence data from Luxembourg. A baseline one-phase SIR model is calibrated by maximum likelihood under a Poisson observation model. The calibrated baseline is then used for conditional comparisons of fixed control regimes, early versus delayed strict intervention, vaccination-supported control, and state-dependent escalation. The results show how switching mechanisms affect both the total number of infected individuals and the extinction time, including their dispersion. Since the switching mechanisms are specified rather than estimated from the intervention history, the results are conditional model-based comparisons rather than estimates of the historical effects of interventions in Luxembourg.

Problem

• epidemic control
• Markovian switching
• state-dependent intervention
• extinction time
• infection burden

Innovation

• Markovian switching
• state-dependent control
• finite-population SIR
• extinction time analysis
• phase-level recursion