Using treatment and vaccination strategies to investigate transmission dynamics of influenza mathematical model

In this study, we built a deterministic compartmental mathematical model for understanding the transmission dynamics of influenza. The model includes multiple infection phases, including susceptible, exposed, carrier, infected, hospitalized, recovered, and vaccinated populations. Real-world epidemiology data calibrate the model using a least squares optimization approach. The model is mathematically well-posed, with demonstrations of existence, uniqueness, positivity, and boundedness of solutions. The basic reproduction number R₀ is computed using the next generation matrix approach. It is found to be 0.480, showing that a single infected individual, on average, infects less than one person in a completely susceptible population. Stability analysis is performed using a Lyapunov function, revealing that the disease-free equilibrium is locally asymptotically stable when R₀<1 and globally stable when R₀>1. Sensitivity analysis suggests that vaccination has a more substantial effect on decreasing transmission compared to treatment. Contour plots of R₀ with respect to key parameters demonstrate that intervention techniques affect epidemic control. Numerical simulations are carried out utilizing the Nonstandard Finite Difference (NSFD) approach to confirm the analytical findings and explore alternative control situations.