# A New Stochastic Model for the _Aedes aegypti_ Life Cycle and the Dengue Virus Transmission
## 4 Discussion  
In this study, we presented a new stochastic model involving all the biological stages, populations, states, and processes that are part of the life cycle of the _Aedes aegypti_ and the dengue virus transmission, such as the oviposited eggs by a blood-fed female, the population in the aquatic phase (larva and pupa), the gender of the population, the mature virgin female and mature virgin male populations, the female and the male populations, the mating of the mosquitoes, the success of a female to be fertilized, and the biting from mosquito to humans. The model also considers populations of uninfected, infected, and bearer but not yet infectious. It is important to remark that the novelty of this model is that it takes into account the three ways reported for the virus transmission, namely, (i) by biting (mosquito-human-mosquito), (ii) by infected mother to its offspring (VT), and (iii) by the venereal transmission from male of infected offspring to virgin female (VNT). Figure 8: Time series of the mean of 100 realizations (in blue) showing the same profile that we can see in 3 aleatory selected realizations (in different colours). The magenta symbols represent the standard deviation for the selected points. In this scenario, five infected females arrive and ovipposit within a human susceptible population wherein the virus can be transmitted by bite, by vertical transmission, and by sexual transmission. In addition, we simulate the implementation of a fumigation-like control that affects only the mosquito population. We show in (**a–d**) the female, male, eggs, and larva populations, respectively. We show in (**e**) the human population; in this case the continuous lines indicate the infected population and the segmented lines show the recovered human population; the colour corresponds to each realization. Some deterministic models have studied epidemic outbreaks and have proposed prevention methods, although they do not consider the temperature-dependent survival of mosquitoes [17; 19]. Other works (also deterministic models) incorporated a seasonal or climatic variation in order to study epidemic outbreaks and control methods [22; 23; 24; 25]. Other deterministic models took into account transovarial transmission (VT) [46; 47], but only [PERSON] et al. [25] consider different sets of temperature. Related to stochastic modelling, three seminal works analysed the evolution of the populations in terms of the biology of the _Aedes aegypti_ and the environment [20; 41; 43]. These models explain the maintenance of the mosquito populations and the persistence of the virus considering the seasonal temperature for Buenos Aires, but they only considered the transmission by biting and the dispersal of the infected _Aedes aegypti_ as the propagation way of the virus. In this line, the new stochastic model we presented in this study addresses the conservation of the virus in a region, i.e., in the mosquito and human populations by considering the three transmission ways, and also in a detailed way all the stages, populations, states and interactions that are involved in the biological life cycle of the mosquitoes--even the success in the reproduction and transmission of the virus from the infected populations. In the scenario where the virus propagation occurs through biting, and 5 infected females looking for a site to oviposit arrive to a susceptible human population, our results show that once these females oviposit and therefore enter the next gonotrophic cycle, the virus can persist for around 65 days, in this scenario the number of infected mosquitoes and infected humans remains low. However, when the virus is transmitted in all the three different ways described in our model, the results show that the infected mosquitoes can survive and grow, infecting the human population (however, there is a recovery parallel process).