Mathematical modeling of the effects of vector control, treatment and mass awareness on the transmission dynamics of dengue fever

Dengue fever is a vital public health concern that affects about 40% of the world’s population. To address the dynamics of dengue disease, a mathematical model was formulated by incorporating three control strategies: vector control, treatment, and mass awareness. A stability analysis of the disease-free equilibrium (DFE) was conducted using the Jacobian matrix. The DFE was found to be locally and globally asymptotically stable when the effective reproductive number was less than one; otherwise, it was unstable. Additionally, an endemic equilibrium point (EEP) was identified. The global stability analysis of the EEP, performed using the Lyapunov method, showed that it is globally asymptotically stable whenever $R_e>1$; otherwise, it is unstable. Bifurcation analysis revealed that the model system exhibits a forward bifurcation. Furthermore, sensitivity analysis of the effective reproduction number revealed that the most sensitive parameters are the biting rate ($b$) and insecticide efficacy ($\delta$). Therefore, the results suggest that, in order to reduce new dengue cases, intervention strategies that decrease the biting rate, such as mosquito repellents and the use of insecticides to kill mosquitoes, should be implemented. Moreover, simulations were conducted for the extended model with vector control, treatment, and mass awareness. The results showed that the combination of vector control, treatment, and mass awareness has a more positive impact on the control of dengue fever than any single or paired intervention. Thus, for effective control of dengue fever, the three control measures should be implemented simultaneously, especially in endemic areas.