Prey-Predator Model with an Infection in both Population: Stability Analysis and an Optimal Control Study - Hariharan, S.; Sreesiva, K.P.; Shangerganesh, L.; Balan, N. Barani (Discontinuity, Nonlinearity, and Complexity, 2026)
In this paper, a preventive model for the treatment of an infectious disease in two animal population, is discussed. First, we study the well-posedness of the proposed mathematical model. Then we determine the disease-free equilibrium point and basic reproductive number of the model. Further, we perform the stability analysis for the disease-free equilibrium point of the model. Next, an optimal control problem is developed to minimize the cost of treating an infected population. Optimality conditions are derived using Pontryagin’s principle. Numerical results are provided to validate the theoretical results.