Modeling influenza transmission and control: epidemic theory insights across Mexico, Italy, and South Africa

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.