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To investigate the spatio-temporal spread of an epidemic in several regions (cities, towns, neighbors...) that are connected by population movements, we adopt a new generalized discrete-time multi-region SIR model, in which we introduce a new diffusion terms that describe the potential attractiveness of each region. In this work we study the effect of the potential attractiveness of regions, and we show the influence of one region on the others by varying attractiveness parameters associated to each zone. We determine an optimal control strategy which allows to reduce the infectious individuals and increase the number of recovered ones in a targeted region and this with an optimal cost. We investigate also the impact of these diffusion parameters on several control strategies by considering several control scenarios. As an application of our theoretical results, first, we investigate the potential attractiveness of the Grand Casablanca-Settat region of Morocco. We calculated the potential attractiveness of each sub region of the studied area by using a qualitative method based on the use of topographic data as well as observations made in the field using the ArcGIS Geoprocessing Tool. The attractiveness map can help to simplify the implementation of control strategies, the organization of cultural events and the implementation of awareness campaigns. Second, we use our new multi-region model to simulate the spread of an epidemic within these connected zones of the Grand Casablanca-Settat region. Examples and numerical simulations are given to illustrate the spread of infection and to illustrate the efficiency of the optimal control strategy. Results of that paper can be used by decision makers to identify and track the evolution of epidemics within a more complex system of connected zones.

communications in mathematical biology and neuroscience

System (GIS) and the mathematical modeling of epidemics to estimate and control the spatio-temporal severity of infection in the most attractive regions