Analysis of Multiple Control Strategies and Prediction of COVID-19 and Influenza Co-Infection by using Neural Networks

The co-infection of COVID-19 and influenza poses a significant public health challenge due to similar clinical presentations and disease severities, posing challenges in diagnosis and management.Biologically, infection with one virus can alter susceptibility to the other, and the harmonic mean incidence function captures the resulting saturation and competition effects in transmission dynamics.This study develops and analyzes a nonlinear deterministic compartmental model describing the co-dynamics of COVID-19 and influenza using the harmonic mean type incidence rate.Analytical results show that the disease-free equilibrium is locally and globally stable when the basic reproduction number less than one.The basic reproduction number is calculated using the nextgeneration method.under baseline parameter values (Table 1), the computed R 0 = max(R 0f ,R 0c ) 2.25, indicating that the co-infection system is in an endemic regime under baseline conditions.Sensitivity analysis reveals that the effective contact rates ( 1 , 2 ) positively influence disease spread, while recovery parameters such , and significantly reduce the reproduction number.To approximate the nonlinear system dynamics, an artificial neural network with Bayesian regularization (ANNs-BRTIN) is trained using synthetic data from the Runge-Kutta ODE45 solver.The neural surrogate reproduces model trajectories with strong agreement, achieving Mean Squared Error values between 9.6610 -4 and 2.9310 -2 , RMSE between 0.031 and 0.171, and MAE between 0.020 and 0.104.Furthermore, optimal control analysis incorporating influenza vaccination, COVID-19 vaccination, and quarantine strategies demonstrates substantial reductions in infected and co-infected populations, indicating that combined interventions can significantly suppress transmission.These findings highlight the effectiveness of integrated control strategies and demonstrate the computational efficiency of ANN-based surrogate modeling for complex epidemic systems.