Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
22 January 2020 |
06 February 2020 |
10 March 2020 |
Abstract: In this work, we devise a multi-regions SL1IL2R discrete-time model which describes the spatial spread of a Mycobacterium Tuberculosis epidemic emerging in regions that are connected by any kind of anthropological movement. The main goal from this kind of modelling, is to exhibit the importance of mobility of individuals, in the spread of infection regardless the mean of transport utilized, and also to show the role of travel restrictions in TB pandemic prevention, by introducing controls variables which reduce the incidence for which an infection could occur once susceptible populations have contacts with infected individuals coming from the neighboring regions of one region targeted by our optimization approach called here: the travel restrictions vicinity optimal control strategy. The theoretical method we follow for the characterization of the travel restrictions optimal controls, is based on a discrete version of Pontryagin's maximum principle while the numerical approach applied to the multi-points boundary value problems we obtain here, is based on discrete progressive-regressive iterative schemes.
