Transmission dynamics of acute respiratory diseases in a population structured by age

Yendry N. Arguedas; Mario Santana-Cibrian; Jorge X. Velasco-Hernández; Yendry N. Arguedas; Mario Santana-Cibrian; Jorge X. Velasco-Hernández

doi:10.3934/mbe.2019375

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 7477-7493. doi: 10.3934/mbe.2019375

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Transmission dynamics of acute respiratory diseases in a population structured by age

1.
Instituto de Matemáticas UNAM (Unidad Juriquilla), Blvd. Juriquilla 3001, Juriquilla, Querétaro, C.P. 76230, Mexico
2.
CONACYT-Instituto de Matemáticas UNAM (Unidad Juriquilla), Blvd. Juriquilla 3001, Juriquilla, Querétaro, C.P. 76230, Mexico

Received: 07 January 2019 Accepted: 07 August 2019 Published: 16 August 2019

Determining the role of age on the transmission of an infection is a topic that has received significant attention. In this work, a dataset of acute respiratory infections structured by age from San Luis Potosí, Mexico, is analyzed to understand the age impact on this class of diseases. To do that, a compartmental SEIRS multigroup model is proposed to describe the infection dynamics among age groups. Then, a Bayesian inference approach is used to estimate relevant parameters in the model such as the probability of infection, the average time that one individual remains infectious, the average time that one individual remains immune, and the force of infection, among others. Based on those estimates, our analysis leads us to conclude that children less than 5 years old are the primary spreaders of respiratory infections in San Luis Potosí's population from 2000 to 2008 since they are more prone to get sick, remain infectious for longer periods and they are reinfected more rapidly. On the other hand, the group of young adults (20-59) is the one that differs the most from the little children's group because it does not get sick often, it remains infectious only a few days and it stays healthy for longer periods. These observations allow us to infer that the group of young adults is the one that, on average, less contributed to the spread of this class of infections during the years represented in our database.
- ARIs,
- bayesian inference,
- inverse problem,
- SEIRS,
- age structured model
Citation: Yendry N. Arguedas, Mario Santana-Cibrian, Jorge X. Velasco-Hernández. Transmission dynamics of acute respiratory diseases in a population structured by age[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7477-7493. doi: 10.3934/mbe.2019375

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Abstract

Determining the role of age on the transmission of an infection is a topic that has received significant attention. In this work, a dataset of acute respiratory infections structured by age from San Luis Potosí, Mexico, is analyzed to understand the age impact on this class of diseases. To do that, a compartmental SEIRS multigroup model is proposed to describe the infection dynamics among age groups. Then, a Bayesian inference approach is used to estimate relevant parameters in the model such as the probability of infection, the average time that one individual remains infectious, the average time that one individual remains immune, and the force of infection, among others. Based on those estimates, our analysis leads us to conclude that children less than 5 years old are the primary spreaders of respiratory infections in San Luis Potosí's population from 2000 to 2008 since they are more prone to get sick, remain infectious for longer periods and they are reinfected more rapidly. On the other hand, the group of young adults (20-59) is the one that differs the most from the little children's group because it does not get sick often, it remains infectious only a few days and it stays healthy for longer periods. These observations allow us to infer that the group of young adults is the one that, on average, less contributed to the spread of this class of infections during the years represented in our database.

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