# A New Stochastic Model for the _Aedes aegypti_ Life Cycle and the Dengue Virus Transmission
## 4 Discussion
We can observe that the profiles of the susceptible, the infected, and the recovery human populations are in agreement to that described by the compartmental models (SIR models) for infectious diseases. As reported by [PERSON] et al. [41], an epidemic outbreak depends on the temperature and on the availability of breeding sites. In this sense, it is noteworthy that the simulations were carried out for the temperature reported for Tuxla Gutierrez, with 6% of the total breeding sites reserved for oviposition of the infected mosquitoes population. It is important to mention that the infected population, in the different stages of the mosquito life cycle, depends of the percentage of breeding sites (in our simulations 6% of the \(BS\) was the minimal value to observe an outbreak). Finally, due to the necessity of implementing control strategies in real life, a fumigation-like control in the mosquito population was applied in our model, which affects the mosquito population. Using this control, the results showed that the infected mosquitoes were extinguished in around 75 days if we implemented the fumigation at least 2 weeks after the first registered contagion, thereby inhibiting the outbreak. In conclusion, the results show that the virus transmission by biting, vertical transmission, and venereal ways produces an outbreak of dengue disease in humans. Our model is a contribution that highlights the fact that considering all the transmission mechanisms of the virus and the environmental conditions could explain the conservation and persistence of the viruses _Flaviviridae_ and _Flavivirus_, leading to a better understanding of the disease and to better control strategies of the propagation of this disease and other related diseases, e.g., chikungunya and zika. In addition, this detailed model could help us understand in a better way the impact on the mosquito population if numerical simulations are carried on, taking into account the control through the sterile insect technique, _Wolbachia_-infected mosquito, or both, since these techniques have been recently tested as control methods [48; 49; 50; 51; 52; 53; 54; 55]. For future contributions, we are currently working on applying our analysis of the _Aedes aegypti_ life cycle and the dengue virus transmission in a 2D model. In this line, numerical simulations are being carried out in a lattice gas model in order to analyse the spatio-temporal dynamics of the infected and uninfected human and mosquito populations. **Author Contributions:** Conceptualization, O.D.-H. and J.-M.C. ; methodology, O.D.-H.; software, O.D.-H.; validation, J.-M.C., J.G.-G. and R.S.-G.; formal analysis, J.-M.C., [PERSON], [PERSON] and [PERSON]; investigation, O.D.-H.; writing--original draft preparation, O.D.-H.; writing--review and editing, [PERSON], [PERSON] and [PERSON]; visualization, O.D.-H.; supervision, O.D.-H. All authors have read and agreed to the published version of the manuscript. **Funding:** This research had no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The codes we used in the present work are available upon reasonable request to the authors. **Acknowledgments:** [PERSON] acknowledges CONACYT (Repatriacion 2019-1). [PERSON] acknowledges CONACYT (Retencion 2019-1). **Conflicts of Interest:** The authors declare no conflict of interest.