Computational analysis of a mathematical model of hookworm infection

According to the Centers for Disease Control and Prevention (CDC) estimates that 576 to 740 million people globally are infected with hookworms. It remains a significant public health threat in tropical and subtropical regions. Especially in low-income countries, hookworm infection continues to affect millions, even with the availability of modern medical advancements. The present study is based on the transmission dynamics of hookworm infection in a population by using the strategy of mathematical modeling with computational methods. The population has been categorized into the following subpopulations such as susceptible humans, infectious humans, infectious humans with heavy infection, humans recovered, worm eggs, non-infective larvae, and infectious larvae and exposed humans. Firstly, the fundamental properties like positivity and boundness are studied. The equilibrium points like hookworm-endemic equilibrium (HEE), hookworm-free equilibrium (HFE), and basic reproduction numbers for the model were computed. Secondly, the stochastic formation of the model was studied with well-known properties like positivity, and the boundedness of the hookworm model. The model has no analytical solution due to the highly complex nonlinearity of the stochastic delay differential equation (SDDEs) of the model. Methods like Euler Maruyama, stochastic Euler, stochastic Runge Kutta, and stochastic nonstandard finite difference are used for its solution and visualization of results. Also, the comparison of standard with nonstandard methods is presented to verify the efficiency of the computational method. Furthermore, the stochastic nonstandard finite difference approximation is a good agreement to restore the dynamical properties of the model like positivity, boundedness, and dynamical consistency. Also, it is shown as efficient, low-cost, and independent of the time step size. In conclusion, the theoretical and numerical results support understanding the transmission dynamics of hookworm infection in the population.