Stochastic disease spreading and containment policies under state-dependent probabilities

Area of Science:

• Epidemiology
• Public Health Policy
• Stochastic Modeling

Background:

• Economic-epidemiological models are crucial for analyzing disease dynamics.
• Disease containment policies, such as treatment, are vital for managing outbreaks.
• Stochastic frameworks capture the inherent uncertainty in disease spread and impact.

Purpose of the Study:

• To analyze the role of disease containment policy (treatment) in a stochastic economic-epidemiological model.
• To investigate how state-dependent probabilities of random shocks influence disease prevalence.
• To determine the optimal policy and steady-state outcomes in the presence of disease shocks.

Main Methods:

• Developed a stochastic economic-epidemiological framework.
• Incorporated state-dependent probabilities for random shocks related to disease prevalence.
• Analyzed the invariant measure and steady-state distribution of disease prevalence.
• Determined optimal treatment policies.

Main Results:

• Treatment policies shift the distribution of disease prevalence towards lower levels.
• State-dependent shock probabilities influence the shape and spread of prevalence distributions.
• Complete disease eradication is unlikely; endemicity prevails in the long run.
• Outcomes can range from highly concentrated low prevalence to broader, potentially higher, prevalence levels.

Conclusions:

• Disease treatment is effective in mitigating prevalence but does not lead to eradication.
• The interplay between treatment policies and shock probabilities shapes long-term disease dynamics.
• Understanding these dynamics is crucial for effective public health interventions and resource allocation.