| Journal: | Latin-American Journal of Computing (LAJC) |
| Database: | |
| System number: | 000565139 |
| ISSN: | 1390-9134 |
| Authors: | Ilha da Silva, Marline1 Marques, Joice Chaves2 Conza, Adelaida Otazu3 De Cezaro, Adriano2 Gomes, Ana Carla Ferreira Nicola2 |
| Institutions: | 1Federal Institute of Rio Grande do Sul, 2Federal Univ. of Rio Grande, Inst. of Mathematics, Statistics and Physics, 3National University of the Altiplano, |
| Year: | 2023 |
| Volumen: | 10 |
| Number: | 2 |
| Pages: | 32-45 |
| Country: | Ecuador |
| Language: | Inglés |
| English abstract | Mathematical models are among the most successful strategies for predicting the dynamics of a disease spreading in a population. Among them, the so-called compartmental models, where the total population is proportionally divided into compartments, are widely used. The SIR model (Susceptible-Infected-Recovered) is one of them, where the dynamics between the compartments follows a system of nonlinear differential equations. As a result of the non-linearity of the SIR dynamics, it has no analytical solution. Therefore, some numerical methods must be used to obtain an approximate solution. In this contribution, we present simulated scenarios for the SIR model showing its stiffness, a phenomenon that implies the necessity of a small step size choice in the numerical approximation. The numerical results, in particular, show that the stiffness phenomenon increases with higher transmission rates and lower birth and mortality rates . We compare the numerical solutions and errors for the SIR model using explicit Euler, Runge Kutta, and the semi-implicit Rosenbrock methods and analyze the numerical implications of the stiffness on them. As a result, we conclude that any accurate numerical solution of the SIR model will depend on an appropriately chosen numerical method and the time step, in terms of the values of the parameters. |
| Keyword: | Numerical Methods, Stiffness, SIR model |
| Keyword: | Numerical Methods, Stiffness, SIR model |
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