5 June 2014 Using special functions to model the propagation of airborne diseases
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Abstract
Some special functions of the mathematical physics are using to obtain a mathematical model of the propagation of airborne diseases. In particular we study the propagation of tuberculosis in closed rooms and we model the propagation using the error function and the Bessel function. In the model, infected individual emit pathogens to the environment and this infect others individuals who absorb it.

The evolution in time of the concentration of pathogens in the environment is computed in terms of error functions. The evolution in time of the number of susceptible individuals is expressed by a differential equation that contains the error function and it is solved numerically for different parametric simulations. The evolution in time of the number of infected individuals is plotted for each numerical simulation. On the other hand, the spatial distribution of the pathogen around the source of infection is represented by the Bessel function K0.

The spatial and temporal distribution of the number of infected individuals is computed and plotted for some numerical simulations. All computations were made using software Computer algebra, specifically Maple. It is expected that the analytical results that we obtained allow the design of treatment rooms and ventilation systems that reduce the risk of spread of tuberculosis.
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Daniela Bolaños, Daniela Bolaños, } "Using special functions to model the propagation of airborne diseases", Proc. SPIE 9112, Sensing Technologies for Global Health, Military Medicine, and Environmental Monitoring IV, 91121O (5 June 2014); doi: 10.1117/12.2049769; https://doi.org/10.1117/12.2049769
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