Optimal control approach to study two strain malaria model

Baba, Bashir Abdullahi; Ismaili, Parvaneh; Baba, Isa Abdullahi

doi:10.1063/1.5136166

Cited by 1 publication

(1 citation statement)

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“…Optimal control is considered as an effective mathematical tool used to optimize the control problems arising in different field including epidemiology, aeronautic engineering, economics, finance, robotics, etc [5]. Mathematical model offers an insight in to the transmission and control of infectious disease [6][7][8][9][10][11][12][13]. Zhao et al [14] developed a Susceptible, Un-quarantined infected, Quarantined infected, Confirmed infected (SUQC) model to characterize the dynamics of COVID-19 and explicitly parameterize the intervention effects of control measures.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Model for the Transmission of Novel COVID-19

Baba¹,

Nasidi²,

Băleanu³

2021

Computers, Materials &Amp; Continua

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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.

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