A multiconsistent computational methodology to resolve a diffusive epidemiological system with effects of migration, vaccination and quarantine.
Comput Methods Programs Biomed
; 236: 107526, 2023 Jun.
Artigo
em Inglês
| MEDLINE | ID: covidwho-20231106
ABSTRACT
BACKGROUND:
We provide a compartmental model for the transmission of some contagious illnesses in a population. The model is based on partial differential equations, and takes into account seven sub-populations which are, concretely, susceptible, exposed, infected (asymptomatic or symptomatic), quarantined, recovered and vaccinated individuals along with migration. The goal is to propose and analyze an efficient computer method which resembles the dynamical properties of the epidemiological model. MATERIALS ANDMETHODS:
A non-local approach is utilized for finding approximate solutions for the mathematical model. To that end, a non-standard finite-difference technique is introduced. The finite-difference scheme is a linearly implicit model which may be rewritten using a suitable matrix. Under suitable circumstances, the matrices representing the methodology are M-matrices.RESULTS:
Analytically, the local asymptotic stability of the constant solutions is investigated and the next generation matrix technique is employed to calculate the reproduction number. Computationally, the dynamical consistency of the method and the numerical efficiency are investigated rigorously. The method is thoroughly examined for its convergence, stability, and consistency.CONCLUSIONS:
The theoretical analysis of the method shows that it is able to maintain the positivity of its solutions and identify equilibria. The method's local asymptotic stability properties are similar to those of the continuous system. The analysis concludes that the numerical model is convergent, stable and consistent, with linear order of convergence in the temporal domain and quadratic order of convergence in the spatial variables. A computer implementation is used to confirm the mathematical properties, and it confirms the ability in our scheme to preserve positivity, and identify equilibrium solutions and their local asymptotic stability.Palavras-chave
Texto completo:
Disponível
Coleções:
Bases de dados internacionais
Base de dados:
MEDLINE
Assunto principal:
Quarentena
/
Modelos Teóricos
Tipo de estudo:
Estudo experimental
/
Estudo observacional
Tópicos:
Vacinas
Limite:
Humanos
Idioma:
Inglês
Revista:
Comput Methods Programs Biomed
Assunto da revista:
Informática Médica
Ano de publicação:
2023
Tipo de documento:
Artigo
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