# Using Mathematical Models to Better Understand Mosquito-Borne Disease Transmission

Reference: Huber, J. H., Childs, M. L., Caldwell, J. M., & Mordecai, E. A. (2018). Seasonal temperature variation influences climate suitability for dengue, chikungunya, and Zika transmission. PLoS neglected tropical diseases12(5), e0006451.  https://doi.org/10.1371/journal.pntd.0006451

##### Introduction:

Dengue, chikungunya, and Zika are all diseases spread in human populations by the Aedes mosquito. Zika can also be spread through sexual contact, but is more commonly spread by mosquitoes. The disease-spreading organism (the mosquito) is called the vector.

The general method of the spreading of disease spread, also known as transmission, common to all three diseases is:

1. A person infected with the disease gets bitten by a mosquito, which sucks in some of the person’s blood. This mosquito is now an infected carrier of the disease.
2. The mosquito bites a person without disease. The bite of the mosquito transmits the disease to this person, who is now infected.
3. The mosquito from step 1 is able to spread the disease to other people in the same manner.
4. Other non-infected mosquitoes biting the person in step two will also become infected, and will be able to spread the disease to other people.
##### How Mathematical Models Can Help

To better study and understand this process and its effects on actual outbreaks of disease, epidemiologists (scientists who study the patterns, causes, and effects of diseases) use mathematical compartmental models. An example is the one below from a paper by John H. Huber and colleagues published in PLOS: Neglected Tropical Diseases.

The top (red) row represents the human population under study (subscript H for human). The bottom (green) row represents the mosquito vector (subscript V for vector).

In both rows:

S = susceptible (those who are not yet infected with the disease and thus could be infected in the future).
E = exposed (those who have been exposed to the disease, but are not yet spreading the disease)
I = infectious (those who can spread the disease)

In contrast, in the human row only:

R = recovered (humans who have recovered from their disease; mosquitoes stay infectious until they die – they never recover.

The solid arrows show the movement of humans from one compartment to the next (following infection, recovery, etc.) The dashed arrows show the pathways of infection.

The researchers used this model, along with data about the diseases, mosquitoes, and historical weather, to study the effects of temperature variation on disease transmission between mosquitoes and humans.

The study results show that the relationship between temperature and the transmission of these disease is not completely straightforward:

At 20 degrees C (gray line), there is no infection (in the SH graph, which represents uninfected people, the gray line doesn’t show a decrease). At 40 degrees C (red line), there is a small decrease in the SH graph, and small increases in the EH and IH graphs – meaning there is a small outbreak of disease.

The highest numbers of both exposed and infected occur at 30 degrees C, with a sharp decrease at 35 degrees C. This shows that mosquitoes spread disease in weather that’s hot, but not too hot.

The researchers showed that the most people infected at any one time and in total during outbreaks occur around 25 degrees C, but the longest outbreak is between 10 and 15 degrees C.

##### What Does This All Mean?

The largest numbers of people are infected with mosquito-borne diseases at 25 to 30 degrees C. However, the time window during which someone could get infected is longest at cooler temperatures. Therefore, a person can still be at risk of getting such diseases even in cooler areas. Finally, the temperature range of a given area has a significant effect on mosquito-borne disease outbreaks.

##### Global Consequences

Huber el 2018. shows the impact through selected cities around the world.

The colors represent how suitable conditions are for a mosquito-borne disease epidemic (blue is the lowest suitability, red is the highest).

Many tropical cities (generally considered at the highest risk of mosquito-borne disease epidemics) are in the red color zone (Rio de Janeiro, Manila, Cali, etc). However, Shanghai, which is not a tropical city is also in the red color zone. So while the location of a city and its general temperature is important for these disease outbreaks, the temperature range (shown on the left of the figure) should also be taken into account.

According to the data in this paper, modeling and predicting of mosquito-borne disease are a lot more interesting – and complicated – than previously thought.

##### Takeaways

According to results of this study, non-tropical areas are no longer immune from mosquito-borne diseases, as was once thought. Also, variations in temperature ranges has a significant effect on disease outbreak length and numbers of people infected during outbreaks.

Climate change is altering existing climate patterns around the world. Already, mosquito-borne diseases are present in areas that they weren’t before. This presents a major challenge to the health systems in those areas, and increases the total global numbers of infected people.

As climate change intensifies and quickens, the resulting changes in temperature are likely to lead to longer and deadlier mosquito-borne disease outbreaks.