Stochastic optimal control of vaccine inventory during epidemics: integrating SEIR dynamics with temperature-driven degradation and uncertain replenishment

Background: Vaccination during epidemics depends on reliable cold chains and timely supply. However, storage temperatures, delivery schedules, and order sizes often fluctuate, and these shifts may erode vaccine integrity and reduce the impact of interventions. Deterministic inventory assumptions can obscure the impact of unpredictable factors, such as product degradation and supply issues, on disease transmission. Method: We formulate a stochastic optimal control model that links a vaccine inventory system with a compartmental SEIR variant. Inventory evolves under temperature-driven wastage and random replenishment, the former represented through Arrhenius kinetics with temperature modeled as a mean-reverting process. A nonstandard finite-difference scheme models the joint epidemic–inventory dynamics. The control problem is posed as a Markov decision process with costs that weigh both health outcomes and logistical performance. Results: Numerical experiments contrast a deterministic baseline with scenarios subject to thermal noise and random replenishment. Temperature variability is likely to induce nontrivial stock losses, while replenishment uncertainty appears to change the timing and intensity of outbreaks. Discussion: Uncertainty in degradation and supply may cause planners to overestimate achievable coverage. Using stochastic processes in inventory–epidemic models may yield more realistic scenarios of scarcity. However, results depend on model structure and data for temperature profiles and lead times. Our simulations suggest that we should incorporate explicit uncertainty quantification into the reliability of the cold chain and the process of inventory replenishment.