A multi-region discrete time mathematical modeling of the dynamics of Covid-19 virus propagation using optimal control

Abstract

We study in this work a discrete mathematical model that describes the dynamics of transmission of the Corona virus between humans on the one hand and animals on the other hand in a region or in different regions. Also, we propose an optimal strategy to implement the optimal campaigns through the use of awareness campaigns in region j that aims at protecting individuals from being infected by the virus, security campaigns and health measures to prevent the movement of individuals from one region to another, encouraging the individuals to join quarantine centers and the disposal of infected animals. The aim is to maximize the number of individuals subjected to quarantine and trying to reduce the number of the infected individuals and the infected animals. Pontryagin's maximum principle in discrete time is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using Matlab. The Incremental Cost-Effectiveness Ratio was calculated to investigate the cost-effectiveness of all possible combinations of the four control measures. Using cost-effectiveness analysis, we show that control of protecting susceptible individuals, preventing their contact with the infected individuals and encouraging the exposed individuals to join quarantine centers provides the most cost-effective strategy to control the disease.

Economic evaluation of programs against COVID-19: A systematic review

“…Six studies performed from the healthcare system perspective ( 4 , 15 , 21 , 25 , 27 , 36 ). Other studies have not stated any perspectives ( 14 , 16 , 17 , 19 , 23 , 24 , 26 , 31 , 32 , 33 , 34 , 35 , 37 , 38 ).…”

“…Overall, 26 articles were included in this review. Most of these studies were from the US (n =9)( 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ), followed by China (n = 4)( 4 , 23 , 24 , 25 ), the UK (n =2)( 26 , 27 ), Germany(n =2)( 28 , 29 ), India (n =2)( 30 , 31 ), Australia (n =1)( 32 ), Israel (n = 1)( 33 ), Morocco (n = 1)( 34 ), Ghana (n = 1)( 35 ), South Africa (n=1)( 36 ), Uganda (n=1)( 37 ), Thailand (n=1)( 38 ).…”

“…Eighteen studies assessed the programs against COVID-19 in the whole population( 4 , 14 , 16 , 20 , 21 , 22 , 23 , 24 , 26 , 28 , 30 , 32 , 33 , 34 , 35 , 36 , 37 ), four studies evaluated preventing programs among patients with COVID-19( 25 , 27 , 29 , 38 ), two studies focused on the healthcare workers (HCWs)( 17 , 18 ), one study on the academic students( 19 ) and last one on the patients with allergic rhinitis( 15 ).…”

“…The three common strategies in most of the included studies were quarantine (n=10)( 4 , 22 , 23 , 24 , 30 , 31 , 33 , 34 , 35 , 36 ), screening and diagnostic tests (n=8)( 17 , 19 , 21 , 25 , 26 , 35 , 36 , 38 ), and social distancing (n=7)( 14 , 15 , 16 , 20 , 24 , 33 , 35 ) which they were evaluated for both target groups (such as high risk or forefront healthcare workers, and academic students) and the general population. A handful of studies evaluated PPE (n = 5)( 17 , 18 , 23 , 35 , 37 ) and isolation (n = 6)( 4 , 22 , 23 , 32 , 34 , 36 ). Three studies examined treatment and vaccination of COVID-19( 20 , 27 , 29 ).…”

Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics

“…where, constants w i , i = 1, 2, ..., 5 are positive weights required to balance the corresponding terms in the objective functional. Following other literature on COVID-19 control problems [9,16,17,40,41], quadratic costs on the controls are chosen, where 1/2w 4 u 2 1 (t) is the total cost of implementing the preventive measure, and 1/2w 5 u 2 2 (t) is the total cost of managing active cases over the time interval [0,…”