Fuzzy Frontiers in Rift Valley Fever Virus Control: Exploring the Dynamics of Transmission and Treatment

Rift Valley Fever (RVF) is a mosquito-borne zoonotic viral disease that poses significant health threats to both human and animal populations across Africa and parts of the Middle East. Traditional epidemiological models often assume precise parameter values, which may not accurately reflect the inherent uncertainty in real-world disease transmission. To address this, we propose a novel stochastic and fuzzy logic-based Susceptible-Infected-Susceptible (SIS) model to analyze the spread of RVF under uncertain conditions. The model incorporates fuzziness in transmission and recovery rates using fuzzy set theory. Equilibrium points are analytically derived, and stability analysis is performed to explore the long-term dynamics of the disease. We compute and compare the fuzzy expectation of infected individuals with the classical expectation to assess the effect of parameter uncertainty. The basic reproduction number is calculated for both strictly increasing and strictly decreasing transmission functions, and their impacts on transcritical and backward bifurcations are thoroughly investigated. Furthermore, we incorporate optimal control strategies, including vaccination and vector control, within the fuzzy framework and evaluate how uncertainty influences their effectiveness. Numerical simulations validate the analytical results and illustrate the temporal progression of the disease. Our findings emphasize that integrating fuzzy logic with stochastic modeling provides a more realistic and robust approach to understanding and controlling RVF than conventional deterministic models, offering valuable insights for public health intervention planning under uncertainty.