This study generalizes the dengue transmission model by considering the dynamics of the human population and the Aedes aegypti mosquito population. The mosquito population is devided into two phases, i.e., the aquatic phase and the adult phase. From the model, we seek the disease-free equilibrium, endemic equilibrium, and basic reproduction number (R0) points. The model yields a single basic reproduction number which determines the system’s behavior. If R0 1, the disease-free equilibrium is locally asymptotically stable, indicating that the disease will die out. Conversely, if R0 1, an endemic equilibrium exists, and the disease may persist in the population. Next, a numerical simulation is performed to geometrically visualize the resulting analysis and also to simulate the dengue transmission in DKI Jakarta Province, Indonesia. The resulting numerical simulation supports our analysis. Meanwhile, the simulation in DKI Jakarta Province suggests that the dengue fever disappears after 60 days from the first case appearance after controlling the mosquito population through fogging and the use of mosquito larvae repellent. Lastly, the sensitivity analysis of R0 indicates that parameters related to the mosquito’s aquatic phase have a strong influence on dengue transmission, meaning that small changes in these parameters can significantly increase or decrease the value of R0 and thus the potential for an outbreak.
Inayah et al. (Mon,) studied this question.