Modeling the effect of memory on the spread of Query fever considering humans, animals and the environment
摘要
This study presents a mathematical model incorporating the effects of memory on the spread of Q fever, considering humans, animals, and environmental contamination of Coxiella burnetii. The model is formulated using a system of fractional-order differential equations with the Caputo fractional derivative to capture the long-term impact of past infections and environmental contamination. A mathematical analysis is performed, including positivity and boundedness of solutions, ensuring biological feasibility. The existence and uniqueness of solutions are established to confirm the model’s well-posedness. Stability analysis is conducted using Hyers–Ulam stability analysis, which guarantees that small perturbations in initial conditions do not lead to significant deviations in the system’s behavior. Sensitivity analysis is carried out to determine the most influential parameters affecting disease transmission, and a sensitivity heat map analysis is used to visualize their impact. From the sensitivity heat map analysis, it is noticed that the model parameters are more sensitive to the susceptible humans,