Mathematical Modelling of the Transmission Dynamics of Scrub Typhus: Optimal Control and Data Driven Analysis

Scrub typhus is a vector-borne infectious disease transmitted to humans through infected chigger mites, with animals serving as important reservoir hosts. This work develops and analyzes a deterministic compartmental model describing the transmission dynamics of scrub typhus among humans, mites, and animals. The model incorporates both horizontal transmission between interacting populations and vertical transmission within the mite population. Positivity and boundedness of solutions are established to ensure well-posedness of the model. The basic reproduction number, R 0 , is derived, and the disease-free equilibrium is shown to be asymptotically stable when R 0 < 1. Further analysis establishes the existence of forward bifurcation. To improve the epidemiological relevance of the study, model parameters are estimated by fitting the infected human population to reported scrub typhus incidence data from Kerala, India, for the period 2014-2023. Sensitivity analysis identifies the key parameters influencing disease transmission. An optimal control framework incorporating vector control, reservoir control, personal protection, and treatment is then investigated. Numerical simulations show that personal protection significantly reduces human infections, while vector control effectively suppresses overall transmission. The combined implementation of all control measures is found to be the most effective strategy. The novelty of the study lies in integrating vertical transmission, data-driven parameter estimation, and multiple optimal control strategies within a unified scrub typhus modelling framework, thereby providing useful insights for public health planning and disease management.