The spreading of Covid-19 in Mexico: A diffusional approach

Abstract

In this work, we analyze the spreading of Covid-19 in Mexico using the spatial SEIRD epidemiologic model. We use the information of the 32 regions (States) that conform the country, such as population density, verified infected cases, and deaths in each State. We extend the SEIRD compartmental epidemiologic with diffusion mechanisms in the exposed and susceptible populations. We use the Fickian law with the diffusion coefficient proportional to the population density to encompass the diffusion effects. The numerical results suggest that the epidemiologic model demands time-dependent parameters to incorporate non-monotonous behavior in the actual data in the global dynamic. The diffusional model proposed in this work has great potential in predicting the virus spreading on different scales, i.e., local, national, and between countries, since the complete reduction in people mobility is impossible.

Keywords: Coronavirus; Covid-19; Diffusion; Mexico; SEIRD model; Spreading.

Fig. 1

Grid mesh employed to discretize the Mexico map.

Fig. 2

Comparison of new infected data per day for Covid-19 and the model results varying the scaling coefficient $D_0$.

Fig. 3

Error as a function of the scaling coefficient $D_0$.

Fig. 4

Numerical estimation of new exposed and infected people per day by Covid-19 in Mexico.

Fig. 5

Estimated new infected and exposed cases per day for some States of Mexico.

Fig. 6

Estimated deaths and recovered people per day.

Fig. 7

Logarithm of exposed people (persons/km²) to Covid-19 for each State of Mexico and as a function of time.

Fig. 8

Intensity of mobility of exposed people around Ciudad de México, at three moments of the pandemic. CM = Ciudad de México, EM = Estado de México, M = Morelos.

Fig. 9

Intensity of mobility of exposed people in the central region of Mexico, at three times of the pandemic. G = Guanajuato, EM = Estado de México, Q = Querétaro, H = Hidalgo.