Analysis of drug-resistant tuberculosis transmission dynamics in China using fractional stochastic model

This study investigates the dynamics of the drug-resistant tuberculosis model through a fractional stochastic modeling framework. The model employs fractional-order derivatives to capture the memory effects in disease transmission, while Brownian motion is introduced to represent the random disturbances, thereby providing a more realistic description of the disease dynamics. First, a fractional deterministic model based on the Atangana-Baleanu-Caputo derivative was developed, and its optimal parameter values were obtained from the actual data from the case of drug-resistant tuberculosis in China. Second, the existence and uniqueness of the solution of the fractional stochastic model were proved, and its numerical solution was explored. Furthermore, the impacts of different interventions strategies on the control of drug-resistant tuberculosis in China were compared. The results demonstrate that the combined interventions exhibit superior efficacy compared to any single intervention. Numerical simulations of deterministic and fractional stochastic models verify the effects of memory and random effects on drug-resistant tuberculosis. It was found that as the noise level increases, the degree of random perturbation in the model solution also increases, and higher noise levels may lead to the early disappearance of drug-resistant tuberculosis.