A Dynamics and Control Study of the New H1N1 Influenza with Two Roots of Infection: The Impact of Optimal Vaccination and Treatment Amar Chatterjee, Santosh Sharma, Fahad Al Basir, Aeshah Raezah Mathematics, 2025 H1N1 influenza, also known as swine flu, is a subtype of the influenza A virus that can infect humans, pigs, and birds. Sensitivity analysis and optimal control studies play a crucial role in understanding the dynamics of H1N1 influenza. In this study, we have derived a mathematical model incorporating both symptomatic and asymptomatic infections, as well as vaccination, to assess the impact of key parameters on disease transmission. Also, we have assumed a density-dependent infection transmission in the modeling process of H1N1 dynamics. We determine the basic reproduction number using the next-generation matrix method and found that the disease-free equilibrium is stable when the basic reproduction number R0<1 and the endemic equilibrium exists and is stable globally when R0>1. By performing sensitivity analysis, the most influential factors affecting infection spread are identified, aiding in targeted intervention strategies. Optimal control techniques are then applied to determine the best approaches to minimize infections while considering resource constraints. The findings provide valuable insights for public health policies, offering effective strategies for mitigating H1N1 outbreaks and enhancing disease management efforts using optimal vaccination.
Impact of awareness in self–monitoring of COVID-19: An optimal control approach Piu Samui, Jayanta Mondal, Amar Nath Chatterjee, Fahad Al Basir Results in Control and Optimization, 2025 COVID-19 has been a significant global health concern since the last quarter of 2019, prompting ongoing research to understand the transmission patterns and develop global intervention methods. This article presents a Scompartmental model that demonstrates the effectiveness of self-monitoring among individuals as a non-pharmaceutical method in reducing infection progression. The existence of equilibria and their stability have been studied on the basic of the basic reproduction number ( R 0 ). We observed forward bifurcation at R 0 = 1 . We have applied optimal control theory and formulated a three control parameters optimal control problem (OCP) to study non-therapeutic measures like increasing awareness of COVID-19 among susceptible and symptomatic individuals and therapeutic measures like providing improved treatment to hospitalized individuals. The cost-effectiveness of these strategies is also analyzed, suggesting the coexistence of possible treatment routes in controlling the virus.
