| dc.description.abstract | A mathematical analysis of influenza virus transmission is undertaken, combining rigorous theoretical development with
numerical simulations informed by real-world data. The terms in the equations introduce parameters which are determined
by fitting the model for matching clinical data sets using nonlinear least-square method. Wave patterns, critical illness fac
tors, and forecasts of influenza transmission at national levels in Mexico, Italy, and South Africa are examined, alongside
evaluations of the effectiveness of existing control measures and proposals for alternative policy interventions. Data for 120
weeks from October 2021 to March 2023 are used to fit the model. Numerical simulations and sensitivity analysis reveal
the effectiveness of various prevention strategies. We performed data fitting using Latin hypercube sampling, sensitivity
indices, Partial Rank Correlation Coefficient (PRCC), and p values to estimate the basic reproduction number R0 and vali
date the model with data from these countries. Leveraging this validation, we identify optimal control strategies involving
antiviral treatment protocols to suppress viral spread, reduce new infections, and minimize systemic costs. The existence
and uniqueness of the optimal control pair are rigorously established, with the derived optimality system solved numerically.
Additionally, we investigated the qualitative behavior of the threshold quantity, which determines whether the disease dies
out or persists in the population. Finally, numerical experiments illustrate the impact of key parameters on transmission
dynamics, corroborating theoretical predictions. | en_US |
