Mathematical Modelling of the Impact of Dengue Fever Using Nonlinear Differential Equations

Dengue fever is a mosquito-borne viral disease that remains a major public health concern in tropical and subtropical regions. This study presents a seven-compartment nonlinear differential equation model comprising four human classes (susceptible, exposed, infectious, and recovered) and three mosquito classes (susceptible, exposed, and infectious) to investigate the transmission dynamics of dengue fever. The model is analysed to establish the non-negativity and boundedness of solutions, determine the biologically feasible region, derive the disease-free equilibrium, and compute the basic reproduction number, $R_0$, using the next-generation matrix method. Local stability analysis of the disease-free equilibrium and the threshold behaviour of the endemic equilibrium are also investigated. The results show that dengue transmission can be eliminated when $R_0<1$, whereas the disease persists when $R_0>1$. The findings emphasize that integrated vector control, environmental sanitation, surveillance, early diagnosis, and effective clinical management are essential for reducing dengue transmission and mitigating future outbreaks.