Optimal Control Model for the Transmission of Novel COVID-19

Abstract

As the corona virus (COVID-19) pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences, optimal control strategy is an effective measure that neutralizes the scourge to its lowest ebb. In this paper, we present a mathematical model for the dynamics of COVID-19, and then we added an optimal control function to the model in order to effectively control the outbreak. We incorporate three main control efforts (isolation, quarantine and hospitalization) into the model aimed at controlling the spread of the pandemic. These efforts are further subdivided into five functions; u 1 (t) (isolation of the susceptible communities), u 2 (t) (contact track measure by which susceptible individuals with contact history are quarantined), u 3 (t) (contact track measure by which infected individualsare quarantined), u 4 (t) (control effort of hospitalizing the infected I 1 ) and u 5 (t) (control effort of hospitalizing the infected I 2 ). We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle. The disease free equilibrium solution (DFE) is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter; basic reproduction number. We constructed Lyapunov function to which global stability of the solutions is established. Numerical simulations show how adopting the available control measures optimally, will drastically reduce the infectious populations.

Sensitivity Analysis of COVID-19 in Mediterranean Island

“…There are other studies that show the importance of control strategies which include awareness, mobility, vaccination rate, etc. [21][22][23]. For future works, effect of medicine can be modelled and analyzed as a treatment of COVID-19.…”

Investigation of time-fractional SIQR Covid-19 mathematical model with fractal-fractional Mittage-Leffler kernel

“…The attention of modeling in fractional differential equations (FDEs), the complex real-world phenomenon is increasing to expecting its many properties which are generally absent in integer-order differential equations. It should be noted that the generalization of the integer order calculus of differential and integral equations to sensible or complex numbers is verified by modern calculus [15] , [16] , [17] , [18] , [19] , [20] . Currently, a lot of mathematical models have been proposed in the area of FC, such that SEIR, HIV, TB, population mathematical representation, cancer representation, predator and prey models, etc.…”

Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

“…The mentioned work is devoted to investigating disease transmission dynamics and their control. In the same fashion to understand the dynamics of COVID-19 and the tracking downof the reasonable result of the outbreak is helpful for public health initiatives and consciousness programs, for which significant work has been published, and we refer to a few such as [9][10][11][12][13][14].…”