Determining the Impact of Exogenous Factors in Acute Respiratory Infections Using a Mathematical Epidemiological Model—Case Study of COVID-19 in a Peruvian Hospital

In this study, we develop and analyze an extended SEIR-type compartmental model that incorporates vaccination and treatment to describe the dynamics of acute respiratory infection transmission. The model subdivides the infectious population into several symptomatic stages and an asymptomatic class, which allows the evaluation of control strategies across different levels of infection severity. The basic reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>0</mn></msub></semantics></math></inline-formula> is analytically derived, and its sensitivity to vaccination and treatment rates is examined to assess the impact of public health interventions on epidemic control. Numerical simulations demonstrate that the joint implementation of vaccination and treatment can markedly reduce disease prevalence and lead to infection elimination when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. The results emphasize the critical role of parameter interactions in determining disease persistence and show that combining both interventions produces stronger epidemiological effects than either one alone. Machine learning techniques, specifically Support Vector Machines (SVMs), are employed to classify epidemiological outcomes and support parameter estimation. The biological markers evaluated were not effective discriminants of infection status, underscoring the importance of integrating mechanistic modeling with data-driven approaches. This combined framework enhances the understanding of epidemic dynamics and improves the predictive capacity for decision-making in public health.