Modelling an SEIR model using saturated treatment function and analysing its stability: the effect of treating H3N2V affected patients by medicines

Swine flu is a respiratory illness characterised by its intense spread during specific seasons, leading to concerns about the potential challenges caused by limited drug availability. This article presents a susceptible-exposed-infected-recovered (SEIR) model incorporating a saturated treatment function to address these concerns. Emphasising the crucial role of early medication in managing the infection, the model serves as a mathematical representation of the disease's dynamics, featuring the novel inclusion of a saturated treatment function to better manage swine flu's transmission challenges. This study emphasises early prescription medicine treatment for infected patients. A thorough methodology verifies the model's positivity and boundedness to ensure it appropriately represents real-world disease dynamics. To better comprehend disease propagation, calculate the reproduction number and find the model's equilibrium locations. The Gershgorin Circle theorem is used to test model stability, showing its capacity to capture disease transmission's complicated dynamics. The essay uses numerical simulations to emphasise the need of timely and proper medicine in preventing illness development. This model-driven technique can avert swine flu pandemics by predicting pharmaceutical needs and reducing supply bottlenecks.