Stochastic Compartmental Models

📉⛈️ Stochastic Differential Equation (SDE) Models: Modeling Noise in Epidemic Trajectories

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Stochastic Differential Equation (SDE) models constitute a powerful class of stochastic compartmental models that extend deterministic epidemic frameworks by explicitly incorporating continuous random perturbations. Rather than assuming fixed transmission and recovery rates, SDEs recognize that epidemiological processes are influenced by ongoing environmental variability, demographic fluctuations, and unobserved behavioral changes. By embedding noise terms directly into … Read more

⏳🎲 Discrete Time Markov Chain (DTMC) Models: Quantifying Epidemic Risk in Generations

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Discrete Time Markov Chain (DTMC) models are a foundational class of stochastic compartmental models in mathematical epidemiology. They are designed to represent epidemic dynamics over fixed, discrete time intervals, such as days or entire generations of infection. Unlike deterministic ordinary differential equation models, DTMCs explicitly incorporate randomness through probability laws, making them particularly suitable for … Read more

🎲📈 Continuous Time Markov Chain (CTMC) Models: Incorporating Stochasticity into Compartmental Epidemiology

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Continuous Time Markov Chain (CTMC) models form a foundational class of stochastic compartmental models in mathematical epidemiology. In contrast to deterministic ordinary differential equation (ODE) models, which describe average behavior in large populations, CTMC models explicitly incorporate randomness through probabilistic transition mechanisms. This allows them to capture demographic stochasticity, chance extinction, and variability in outbreak … Read more