Publicação

Fractional differential equations of a reaction-diffusion SIR model involving the Caputo-fractional time-derivative and a nonlinear diffusion operator

Ver documento

Detalhes bibliográficos
Resumo:The main aim of this study is to analyze a fractional parabolic SIR epidemic model of a reaction-diffusion, by using the nonlocal Caputo fractional time-fractional derivative and employing the $p$-Laplacian operator. The immunity is imposed through the vaccination program, which is regarded as a control variable. Finding the optimal control pair that reduces the number of sick people, the associated vaccination, and treatment expenses across a constrained time and space is our main study. The existence and uniqueness of the nonnegative solution for the spatiotemporal SIR model are established. It is also demonstrated that an optimal control exists. In addition, we obtain a description of the optimal control in terms of state and adjoint functions. Then, the optimality system is resolved by a discrete iterative scheme that converges after an appropriate test, similar to the forward-backward sweep method. Finally, numerical approximations are given to show the effectiveness of the proposed control program, which provides meaningful results using different values of the fractional order and $p$, respectively the order of the Caputo derivative and the $p$-Laplacian operators.
Autores principais:Zinihi, Achraf
Outros Autores:Ammi, Moulay Rchid Sidi; Torres, Delfim F. M.
Assunto:Fractional differential equations Epidemic model Caputo fractional derivatives p-Laplacian operator Optimal control Numerical approximations
Ano:2025
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso restrito
Instituição associada:Universidade de Aveiro
Idioma:inglês
Origem:RIA - Repositório Institucional da Universidade de Aveiro

Registos relacionados

Registos relacionados