(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The aim of this study is to construct and investigate a mathematical model to grasp the dynamics of dengue fever and assess the consequences of vaccine and treatment approaches in disease control. We created a mathematical model, including human and mosquito populations, using impulsive differential equations to simulate vaccination and antiviral treatment interventions. We used the stability analysis of equilibrium points to find the behavior of the system under different situations. We used MATLAB to run numerical simulations evaluating several intervention possibilities. Particularly when started early on, immunization programs dramatically lower dengue transmission rates. Moreover, combining vaccination with antiviral medications increases the efficacy of intervention campaigns, therefore accelerating the decrease in disease prevalence and enhancing long-term control of epidemics. Effective control of dengue depends on integrated programs combining immunization and antiviral therapies. Reducing the public health load of dengue fever and stopping transmission depend on early intervention and constant efforts.