We propose several spatial-temporal epidemiological mathematical models to study their suitability to approximate the dynamics of the early phase of the COVID-19 pandemic in Chile. The model considers the population density of susceptible, infected, and recovered individuals. The models are based on a system of partial differential equations. The first model considers a space-invariant transmission rate, and the second modeling approach is based on different space-variant transmission rates. The third modeling approach, which is more complex, uses a transmission rate that varies with space and time. One main aim of this study is to present the advantages and drawbacks of the mathematical approaches proposed to describe the COVID-19 pandemic in Chile. We show that the calibration of the models is challenging. The results of the model's calibration suggest that the spread of SARS-CoV-2 in the regions of Chile was different. Moreover, this study provides additional insight since few studies have explored similar mathematical modeling approaches with real-world data.
Citation: Gilberto González-Parra, Cristina-Luisovna Pérez, Marcos Llamazares, Rafael-J. Villanueva, Jesus Villegas-Villanueva. Challenges in the mathematical modeling of the spatial diffusion of SARS-CoV-2 in Chile[J]. Mathematical Biosciences and Engineering, 2025, 22(7): 1680-1721. doi: 10.3934/mbe.2025062
We propose several spatial-temporal epidemiological mathematical models to study their suitability to approximate the dynamics of the early phase of the COVID-19 pandemic in Chile. The model considers the population density of susceptible, infected, and recovered individuals. The models are based on a system of partial differential equations. The first model considers a space-invariant transmission rate, and the second modeling approach is based on different space-variant transmission rates. The third modeling approach, which is more complex, uses a transmission rate that varies with space and time. One main aim of this study is to present the advantages and drawbacks of the mathematical approaches proposed to describe the COVID-19 pandemic in Chile. We show that the calibration of the models is challenging. The results of the model's calibration suggest that the spread of SARS-CoV-2 in the regions of Chile was different. Moreover, this study provides additional insight since few studies have explored similar mathematical modeling approaches with real-world data.
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Figures(19) / Tables(3)
Gilberto González-Parra, Cristina-Luisovna Pérez, Marcos Llamazares, Rafael-J. Villanueva, Jesus Villegas-Villanueva. Challenges in the mathematical modeling of the spatial diffusion of SARS-CoV-2 in Chile[J]. Mathematical Biosciences and Engineering, 2025, 22(7): 1680-1721. doi: 10.3934/mbe.2025062
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