Optimal control strategy of SEIR endemic model with continuous age‐structure in the exposed and infectious classes

Khan, Asaf; Zaman, Gul

doi:10.1002/oca.2437

Cited by 26 publications

(15 citation statements)

References 29 publications

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“…We prove that there is a solution to problem (24) – (26) , which exists. So clearly the control functions are Lebesgue measurable and not negative, therefore with nonnegativity of initial data it is very handy to investigate that a solution with the axiom of bounded-ness and positivity exists, for example see for more detail [24] , [25] , [26] .…”

Section: Optimal Control Analysismentioning

confidence: 99%

Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China

Din

Khan

et al. 2020

Chaos, Solitons & Fractals

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117

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Number of well-known contagious diseases exist around the world that mainly include HIV, Hepatitis B, influenzas etc., among these, a recently contested coronavirus (COVID-19) is a serious class of such transmissible syndromes. Abundant scientific evidence the wild animals are believed to be the primary hosts of the virus. Majority of such cases are considered to be human-to-human transmission, while a few are due to wild animals-to-human transmission and substantial burdens on healthcare system following this spread. To understand the dynamical behavior such diseases, we fitted a susceptible-infectious-quarantined model for human cases with constant proportions. We proposed a model that provide better constraints on understanding the climaxes of such unseen disastrous spread, relevant consequences, and suggesting future imperative strategies need to be adopted. The main features of the work include the positivity, boundedness, existence and uniqueness of solution of the model. The conditions were derived under which the COVID-19 may extinct or persist in the population. Sensitivity and estimation of those important parameters have been carried out that plays key role in the transmission mechanism. To optimize the spread of such disease, we present a control problem for further analysis using two control measures. The necessary conditions have been derived using the Pontryagin’s maximum principle. Parameter values have been estimated from the real data and experimental numerical simulations are presented for comparison as well as verification of theoretical results. The obtained numerical results also present the verification, accuracy, validation, and robustness of the proposed scheme.

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Section: Optimal Control Analysismentioning

confidence: 99%

Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China

Din

Khan

et al. 2020

Chaos, Solitons & Fractals

Self Cite

117

View full text Add to dashboard Cite

show abstract

“…Thus, we can say that the new dependent variable a is a dynamical variable whose dynamics is given by da dt = 1. Keeping in view the ideas of [12,22,24,25], we have developed a flow diagram (see Fig. 1) which represents the inflow and outflow of population to each compartment.…”

Section: The Modelmentioning

confidence: 99%

“…As the problem under consideration is stated in an infinite-dimensional space, we will apply optimal control theory since it is dynamic. As suggested in [24], we will use the maximum principle type results introduced by Li and Yong [28].…”

Section: Optimal Control Strategiesmentioning

confidence: 99%

Controlling heroin addiction via age-structured modeling

Din

2020

Adv Differ Equ

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The aim of the present study is to consider a heroin epidemic model with age-structure only in the active heroin users. The model was formulated with the help of available literature on heroin epidemic. Instead of treatment as a class, we incorporated recovered population and considered treatment as a control variable and thus a control problem is presented for further analysis. The techniques of weak derivatives and sensitivities were used for obtaining the adjoint equations. The maximum principle of Pontryagin’ type was used for obtaining the optimal value of the control variable. Sample simulations are presented at the end of the study in order to show the effectiveness of the treatment.

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“…In addition, the theory of FOCPs has been under development. Recently, some interesting real-life models of optimal control problems (OCPs) were presented elsewhere [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52].…”

Section: Introductionmentioning

confidence: 99%

Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains

Sweilam

AL–Mekhlafi

Băleanu

2019

Journal of Advanced Research

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Optimal control strategy of SEIR endemic model with continuous age‐structure in the exposed and infectious classes

Cited by 26 publications

References 29 publications

Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China

Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China

Controlling heroin addiction via age-structured modeling

Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains

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