SEIRS Reaction-Diffusion Model

• Autor(a) principal: Castelhano, Alice Neves
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10362/150516
• topic: Spatial heterogeneity; -SEIRS model; Basic reproduction number; Diseasefree equilibrium; Endemic equilibrium; SARS-Cov-2; Domínio/Área Científica::Ciências Naturais::Matemáticas

This thesis seeks to understand the effect of the inclusion of spacial heterogeneity in a SEIRS transmission model by considering a reaction-diffusion SEIRS model. Heterogeneity may correspond to different factors such as the different age classes, contact or spatial matrices, stage of the disease or behaviour. The model in study is suitable for a non-homogeneous population in which the epidemiological parameters depend on the spatial position of each individual. A spatial SEIRS reaction-diffusion model is developed and we focus our theoretical study in the existence of solutions for the equilibrium problem of the epidemic model and their respective steady states. First a global solution of the model is shown to exist. The disease free equilibrium (DFE) is established and its asymptotic profiles determined depending on the basic reproduction number, R0, is defined for two distinguished problems - one with all diffusion coefficients set as positive constants and the other with some diffusion coefficients equal to zero. It is shown for both epidemic problems that if R0 < 1 then the DFE is locally asymptotically stable, else it is unstable. A numerical method based on finite difference schemes is considered to approximate the solution of the reaction-diffusion system of equations and using the proposed method we present simulations that illustrate the theoretical results stated in the previous chapters. Lastly, the model is parameterized according to studies for COVID-19 transmission dynamics in Portugal. Here, we illustrate the model predictions for the non-spatial and spatial case. Furthermore, different scenarios for the implementation of non-pharmacological interventions are illustrated from February 2020 to June 2020. Simulations suggest that the lockdown imposed in Portugal on the 18th of March 2020 reduced the number of infected individuals in approximately 254490 daily cases.