A multi-regions discrete-time epidemic model with a travel-blocking vicinity optimal control approach on patches

Advances in Difference Equations

Samih Lazaiz¹  Ilias Elmouki²  Omar Zakary²  Mostafa Rachik² 

[1] Laboratory of Algebra, Analysis and Applications (L3A), Department of Mathematics and Computer Science, Hassan II University of Casablanca, Casablanca, Morocco;Laboratory of Analysis, Modeling and Simulation (LAMS), Department of Mathematics and Computer Science, Hassan II University of Casablanca, Casablanca, Morocco

关键词: multi-regions model;    SIR epidemic model;    discrete-time model;    optimal control;    vicinity;    travel-blocking;   

DOI  :  10.1186/s13662-017-1168-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study, in this paper, infection dynamics when an epidemic emerges to many regions which are connected with their neighbors by any kind of anthropological movement. For this, we devise a multi-regions discrete-time model with the three classical SIR compartments, describing the spatial-temporal behaviors of homogenous susceptible, infected and removed populations. We suppose a large geographical domain, presented by a grid of colored cells, to exhibit at each instant i the spatial propagation of an epidemic which affects its different parts or sub-domains that we call here cells or regions. In order to minimize the number of infected individuals in some regions, we suggest an optimal control approach based on a travel-blocking vicinity strategy which aims to control a group of cells, or a patch, by restricting movements of infected people coming from its neighboring cells. We apply a discrete version of Pontryagin’s maximum principle to state the necessary conditions and characterization of the travel-blocking optimal controls. We provide cellular simulations based on discrete progressive-regressive iterative schemes associated with the obtained multi-points boundary value problems. For illustrating the modeling and optimal control approaches, we consider an example of 100 regions.

【 授权许可】

CC BY