A New Stochastic Model for the Aedes aegypti Life Cycle and the Dengue Virus Transmission

Dengue is a viral infection transmitted mainly by the Aedes aegypti mosquito and to a lesser extent by the Aedes albopictus. This infectious disease generally causes flu-like symptoms, but it can also lead to life-threatening symptoms. Unfortunately, the number of cases increases every year and about a third part of the world's population is at risk of contracting this disease. To generate tools capable of containing dengue transmission, we present a novel stochastic model for the Aedes aegypti life cycle and the dengue virus transmission, taking into account all the mechanisms of transmission and parameters estimated experimentally to date. This new model describes in detail all the interactions in the stages of the life cycle of the mosquito. It also considers the environmental conditions, i.e., the breeding sites and the temperature, which are very important factors for the mosquito survival. The results show that the contagion by bite only does not provoke an epidemic outbreak when five infected, pregnant, and fed females, looking for lay eggs, arrive to a susceptible human population. However, if in addition to the bite transmission, the virus is also transmitted in vertical transmission and sexual ways, then an outbreak arises. Altogether, the transmission mechanisms and the adequate environmental conditions could explain the virus persistence in the population. Under these conditions and by considering fumigation as a way to control the mosquito population, in this new model the outbreak and the virus propagation could be avoided-but only if the control is implemented within the first two weeks of the presence of the virus.