In this paper written in mid 2021, we presented the standard model for malaria based on an SIR model. The funnest part, however, was generalizing this model to include the introduction of genetically modified mosquitoes into the system. The idea for this generalization is rooted in this Nature article, that covers how genetically modified male mosquitoes can potentially reduce the spread of vector borne diseases, in particular malaria. Of course, we made some simplifications and assumptions but the end result was a complete success!
You can find the introduction below, contact me if you are interested in other parts of the paper!
Since its inception, the medical sector has faced many challenges that require prompt and well-devised measures, given the major repercussions that can take place at the level of our society. One of the most tested branches of medicine has proved to be epidemiology, due to the wide range of pathological agents that constantly attract the attention of researchers. This field, in combination with mathematics, has given rise to models used to analyze the spread of diseases. One such disease that has been studied numerous times is malaria, because of the persistence it has presented to this day and the lack of a cure. Recently, genetically modified mosquitoes have been developed with the specific intention of combating malaria and other vector-borne diseases. These genetically modi- fied male mosquitoes breed with other mosquitoes causing the resulting female larvae to die, which reduces the amount of female mosquitoes which are the main vector for malaria.
With the goal of better understanding how the spread of malaria can be pre- vented, saving millions of lives in the process, this paper provides the stan- dard malaria model, develops a model for how the genetic modification spreads through the mosquito population, and finally combines both models to study the impact that genetic intervention has on the complete system.