Mathematical modeling and dynamic analysis of dengue fever: examining economic and psychological impacts and forecasting disease trends through 2030—a case study of Nepal

Dengue fever is a viral disease predominantly found in tropical and subtropical regions. The mild form presents with fever and flu-like symptoms, whereas the severe form can cause significant bleeding, a drastic drop in blood pressure, and even death. A mathematical model was developed consisting of ten classes: seven for humans and three for mosquitoes. The model was then reduced to eight classes to better simulate the transmission dynamics of the dengue virus. In numerical experiments, it was fitted to dengue infection data from 2022 and from 2004 to 2022 in Nepal using the least squares method. Sensitivity analysis identified the parameters with the most significant influence on the basic reproduction number. Conclusions The model has been validated to ensure the positivity and boundedness of solutions. The basic reproduction number ([Formula: see text]) was derived using the next-generation matrix approach. We have analytically and graphically demonstrated that both the Dengue-free and endemic equilibrium points are locally and globally stable. Additionally, the presence of a forward bifurcation was confirmed through the Center Manifold theory. Sensitivity analysis identified the parameters with the most significant influence on the basic reproduction number. Finally, the model equations were numerically solved using the Runge-Kutta (ODE45) method to assess the impact of key parameters on the system's behavior. Moreover, we analyzed the economic and psychological effects of dengue fever on hospitalized patients in Nepal from 2004 to 2022 and projected the disease trend through 2030. Furthermore, this study was compared with the three other articles in terms of methodology and model design.