Fractional-Order Mathematical Modeling of Human Papilloma Virus (HPV) Using Artificial Deep Neural Networks

The study proposes a mathematical framework to evaluate the HPV infection transmission dynamics, taking into account advanced approaches related to fractional calculus. The HPV infection and cervical cancer is always a major public health threat across the world, particularly in those areas having insufficient availability to health care services and control interventions. In first step, the positivity and boundedness of solutions are precisely examined to show that the model remains biologically valuable in the long run. In this study the disease free equilibrium and endemic equilibrium is provided to describe the long term behavior of the disease in a population. The basic reproductive number and sensitivity analysis is also studied as it is vital to analyse behavior of the dynamics. The theoretical results is establish for the model under consideration using fixed point theory. Next, the condition for Hyers-Ulam’s (H-U) type stability is clearly demonstrated. Then, applying the modified Euler’s method (MEM) for the computation of numerical solution of the proposed model. At the end, we give graphical representation of the involved results. We use some real values for the parameters involved in our considered model. Matlab is used for graphical demonstration. Through a comprehensive numerical analysis, the model explores how various fractional order values inuence the dynamics of HPV transmission. Hence, revealing suggestions for how fractional order may better convey the intricate relationships within the communities. These development also draw awareness to the method’s significance in advancing disease modeling and deepening our knowledge of HPV transmission. With the help of artificial deep neural networks (DNNs), we investigate the considered model. We deduced some statistical thresholds including mean squared error (MSE) and root mean squared error (RMSE) together with progressional analysis. Further, graphical illustrations are given for infected classes using different fractional order. Absolute error between the simulated and those predicted by DNNs are compared for various fractional orders.