# How Human Mobility Models Can Help to Deal with COVID-19
## 6 Analysis of COVID-19 Transmission
### Background
For example, a contagious individual, with a greater lung capacity or breathing rapidly, may emit a greater volume of aerosol, and, thus he/she emits with greater intensity or with a higher emission rate. This aerosol is rapidly diluted with distance and degrades with atmospheric agents. At a shorter distance, the viral concentration will be greater and the action of atmospheric agents will be less noticeable. Finally, another important factor of the virus transmissibility is the quality of the medium (\(Q_{m}\)). A more aggressive medium (for the virus) where we can find UV radiation, a higher concentration of oxygen or chloride ions will reduce its effective transmission. On the contrary, a colder environment, air at rest, without direct sunlight will promote transmission of the virus. Virus transmission at low temperatures is more intensified by the ability of the air to maintain aerosols at lower temperatures. Furthermore, indoors the air is at rest, and the diffusion is uniform so the risk increases. Therefore, ventilation is a key element in reducing the risk of virus transmissibility. The medium can be analysed in greater detail. As previously said, exposure intensity will be lower in open or ventilated premises compared to enclosed ones. This intensity can be reduced in closed premises through well-designed air recirculation systems. Nevertheless, low temperature allows the aerosol to remain in the environment for longer. For example, there have been many COVID-19 outbreaks in meat and cold cut processing plants. In such places, the indoor temperature may be below dew temperature and air conditioning recirculation systems can distribute potentially contaminated air to all rooms. Summing up, the exposure risk (\(ER\)) will be proportional to the exposure time \(t\) and the exposure intensity \(I_{x}\):  
\[ER=K\cdot t\cdot I_{x} \tag{1}\]  
where \(K\) is a constant for adjusting the model. For determining how the exposure intensity \(I_{x}\) depends on the distance \(d\), we employ a simple physical model of the dispersion of particles (in this case, the virus in aerosols). Concretely, we consider that diffusion decayswith the squared distance from the emitter. Consequently, \(I_{x}\) is proportional to the emitter intensity (\(I_{e}\)) and inversely proportional to the square of the distance (\(d\)) between the individuals:  
\[I_{x}=Q_{m}\frac{I_{e}}{d^{2}} \tag{2}\]  
where \(Q_{m}\) is a factor which depends on the quality of the medium. In our model, as we want to obtain a spatial and temporal evaluation of the exposure risk, we consider that all people in the scenario to evaluate are potentially infectious. Of course, the real risk will depend on the real number (or density) of contagious people in the scenario. Indeed, in a place with no contagious people, the real risk will be zero. The idea is that each contact can be risky (when you enter a place, you do not know if there are contagious people or not and who they are). Assuming also that the intensity of the emission is the same for all emitters, we can simplify the previous expression, considering \(I_{e}\) to be one. This is the same approach that other authors make when considering the quanta emission rate to be constant [28]. Thus, combining Expression (1) with the simplified expression of \(I_{x}\), we have:  
\[ER=K\cdot Q_{m}\frac{t}{d^{2}} \tag{3}\]  
Thus, using this expression we can obtain the exposure risk to the COVID-19 infection. This risk, understood as the possibility that a person could be infected, depends on the quality of the medium and is directly proportional to the time and inversely proportional to the square of the distance that separates the person from the contagious individual. Now, we will characterise the quality of the medium as the factor \(Q_{m}\), based on the study of [PERSON] et al. [31] about the physical conditions which impact the SARS-CoV-2 virus airborne transmission.