Mathematical modelling and analysis of human metapneumovirus transmission dynamics using neural network intelligence and optimal control.

Human metapneumovirus (hMPV) is a serious global health threat because it causes human respiratory diseases in people of all ages. The complicated dynamics of this virus transmission exist in complications of waning immunity and reinfection that are extremely problematic for mathematical epidemiology. The aim of this research is to develop an integrated approach that combines a fractional-order mathematical model of hMPV transmission with a computational framework that forecasts outbreaks and optimal control, which applies effective control measures and captures complex immunological memory effects. This study presents a novel eight-compartment S0EIsIaHR1S1R2+ mathematical model that incorporates some complex transmission pathways, like naive susceptible, asymptomatic, initially recovered, susceptible with immunity, and recovered with immunity. We examine the model's mathematical validity by demonstrating its well-posedness, boundedness, and non-negativity. We use the next-generation matrix to estimate the basic reproduction number R0, as well as the hMPV-free and endemic equilibrium points. Moreover, we conduct a complete stability analysis of both disease-free and endemic equilibrium. According to a global sensitivity analysis, the transmission rate β (+0.788), symptomatic recovery rate γs (-0.394), and symptomatic proportion p (+0.234) have the greatest effects on R0. Also, inspired by physics-informed neural networks, a modified disease-informed neural network architecture is designed to overcome the shortcomings of traditional computational methods by including physical constraints into the training procedure. Using synthetic data for validation, our analysis demonstrates an excellent predictive performance with R2 values ranging from 0.8500 to 0.9800 across all test scenarios, and the average error accuracy of compartments stays extremely low with MSE≤0.0443 across multiple independent trials. Furthermore, our optimal control analysis validates that a synergy of intervention strategies achieves a 47.3% reduction in the peak hospitalizations of the model compared to the baseline model estimates. These results offer practical insights for public health policies, highlighting the significance of enhanced screening for symptoms and asymptomatic conditions, immunity maintenance initiatives, and effective control methods. This unified framework gives public health officials a useful tool to test intervention methods and forecast outbreaks using this innovative method that links mathematical models with real-world information.