Abstract:
Optimal control theory and evolutionary game theory are essential tools for comprehending and influencing the intricate behaviors of complex systems, particularly in the context of disease transmission and strategies for intervention. In this study, optimal control theory is leveraged to address short-term disease dynamics using a single-season strategy, while evolutionary game theory guides the approach on a longer timescale through a repeated seasonal model. A system of nonlinear ordinary differential equations is employed to dissect how the dynamics of primary infections impact the spread of Nipah disease in our novel dynamic system, extending the classical Susceptible-Infected-Recovered (SIR) model by introducing four distinct population categories: humans, bats, fruit, and animals.We delve into this epidemic model's theoretical underpinnings, examining disease-free and endemic equilibria to establish stability conditions. To address the challenge of optimally reducing the number of infectious individuals, we formulate an optimal control problem featuring four distinct control strategies. These strategies are deployed to mitigate disease transmission, all driven by a generalized incidence function. By identifying the optimal amalgamation of these strategies, we aim to minimize the infectious population. Decisions about the selection and execution of diverse disease control policies rest upon theoretical projections and numerical simulations conducted over a single season. Our study also incorporates evolutionary game dynamics, wherein individuals choose whether to adopt awareness and protection measures after the disease has circulated within the community. We meticulously explore the impact of such awareness and protection measures to underscore their significance within the context of the epidemic model across multiple time steps. Moreover, we systematically analyze the parameter properties within the epidemic model to address diverse real-world scenarios.
