Optimal Control and Bayesian Parameter Estimation of a Nonlinear Compartmental Epidemic Model

Late blight, caused by the oomycete Phytophthora infestans , significantly threatens tomato cultivation. In this work, we propose a modified SEIR‐type compartmental model with four epidemiological stages to capture the progression of the disease. A detailed mathematical analysis is carried out, establishing the model's positivity, boundedness, and the existence and stability of both disease‐free and endemic equilibria. Parameter estimation is performed using Bayesian inference via Markov chain Monte Carlo (MCMC), ensuring consistency with empirical data. We then formulate and solve an optimal control problem using Pontryagin's maximum principle, aiming to reduce disease prevalence and control‐related costs. The model incorporates a mobile app–based intervention strategy as a time‐dependent control variable. This study highlights the effectiveness of combining rigorous mathematical modeling, data‐driven calibration, and optimal control to inform the management of plant disease epidemics.