A hybrid quantum-classical framework for nonlinear hookworm transmission dynamics using variational quantum algorithms

Hookworms are parasitic worms infecting approximately 406–480 million people worldwide, named for their hook-like mouthparts. Infection occurs when larvae from contaminated soil penetrate the skin or are ingested, developing into adult worms in the small intestine. This study presents a nonlinear mathematical model for the transmission dynamics of hookworm infection that incorporates multiple classes of human infection and stages of environmental parasites. The model is a nonlinear system that describes the interactions between susceptible, exposed, moderately and heavily infected people, as well as eggs and larval in the environment, resulting in a highly coupled system. Qualitative analysis is carried out to determine the basic properties of the model such as positivity, boundedness, and presence of equilibrium points. Basic reproduction number is calculated to find out the threshold factors on the persistence and elimination of the disease. A hybrid quantum-classical computational scheme using variational quantum algorithms is introduced to solve the complexity of the nonlinear system. It combines quantum circuit generated trial functions with parameters and converts the system to a residual-based optimization problem. This approach enables efficient approximation of the system dynamics through classical optimization of quantum circuit parameters. The temporal behavior of the model in biologically relevant parameter values is investigated in numerical simulations. The findings indicate how the nonlinear interactions between the human and the environmental compartments play a significant role in maintaining the transmission dynamics. The research potential of hybrid quantum-classical methods as a new computational tool to address complicated epidemiological models is emphasized and serves as a basis of future developments with the inclusion of stochastic effects and spatial heterogeneity.