In this paper we develop a probabilistic framework for quantifying the economic impact of epidemics under prevalence-based control policies. The epidemic dynamics are described by a novel continuous-time Markovian SIR model in which the infection rates and the cost structure switch when the number of infectious cases crosses a critical threshold. On top of the stochastic dynamics, we consider a state-dependent cost framework that distinguishes (i) time-in-state sojourn costs, (ii) per-infection costs and (iii) activation/deactivation expenses associated with implementing and lifting control measures. Within this setting, we define the total epidemic cost and the cost of a tagged infectious individual as random variables and derive recursive expressions for their Laplace–Stieltjes transforms (LSTs) and moments. Using matrix differential calculus and Kronecker products, we further obtain recursive formulas for the sensitivities and elasticities of the most representative moments, with respect to the main cost parameters. Numerical experiments illustrate how different cost components drive the mean and standard deviation of total and individual costs across a range of thresholds and epidemic scenarios. The proposed methodology thus combines stochastic epidemic modeling and perturbation analysis to provide distribution-aware, parameter-sensitive assessments of epidemic costs, with direct relevance for statistical evaluation and operations research methods in policy design.
Vasileios E. Papageorgiou, A. Economou· Methodology and Computing in...· 0 citations
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.
Vasileios E. Papageorgiou, Irène Votsi, Samis Trevezas· 0 citations
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