Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model

Abstract

It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.

Optimal control analysis of COVID-19 vaccine epidemic model: a case study

“…Proof The results in (15) are obtained for the Hamiltonian function given in (13), by using transversality conditions and Pontryagin's maximum principle conditions given in (14). Moreover, the optimal controls u * 1 , u * 2 and u * 3 in ( 15) are computed, by implementing the condition…”

“…The optimal control analysis for the outbreak of coronavirus in the USA was carried out by Calvin et al [ 12 ], using SEAIR mathematical model. An epidemic model was designed Takasar et al [ 13 ], that predict future situation based on the number of infected cases and predicted the outcomes on the reported infected cases in Pakistan. The authors carried out sensitivity and optimal control analysis based on the proposed model.…”

Investigating the trade-off between self-quarantine and forced quarantine provisions to control an epidemic: An evolutionary approach

“…Since its creation by Kermack and McKendrick, the model has been thoroughly explored and expanded to meet a variety of hypotheses and situations [9] . Some epidemics, for example, may demand the addition of additional compartments, such as those harboring exposed, asymptomatic agents, Quarantined agents, Hospitalized agents (known as SEIR, SEAIR, SEIAQR, SEIAQHR models respectively) [ 9 , [42] , [43] , [44] , [45] ]. Other applications for compartmental models in epidemiology include the investigation of control and mitigation techniques such as vaccination, the modeling of vector-borne diseases, and the effects of birth and death dynamics [ 9 , 39 ].…”

Socio-demographic and health factors drive the epidemic progression and should guide vaccination strategies for best COVID-19 containment

“…This has stimulated an unprecedented interest in epidemiological models, especially predicting the outcomes of scenarios considering counter- and prevention measures, in particular the forthcoming vaccination. Complex systems and network science approaches, along with technological advances and data availability, are becoming instrumental for the design of effective containment strategies [3] , [4] , [5] , [6] , [7] . Numerous recent works are devoted to fitting of the available data [8] , [9] , inferring the key epidemiological processes [10] , [11] , [12] , identifying the control knobs for non-pharmaceutical interventions [13] , [14] , aiding decisions on emergency management [15] , [16] , checking the effectiveness and importance of lockdowns [17] and making predictions about the further epidemic progression [18] , [19] , [20] , with the aim to support the decision-making process amid the crisis.…”