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

Abstract

The purpose of this research is to explore the complex dynamics and impact of vaccination in controlling COVID-19 outbreak. We formulate the classical epidemic compartmental model by introducing vaccination class. Initially, the proposed mathematical model is analyzed qualitatively. The basic reproductive number is computed and its numerical value is estimated using actual reported data of COVID-19 for Pakistan. The sensitivity analysis is performed to analyze the contribution of model embedded parameters in transmission of the disease. Further, we compute the equilibrium points and discussed its local and global stability. In order to investigate the influence of model key parameters on the transmission and controlling of the disease, we perform numerical simulations describing the impact of various scenarios of vaccine efficacy rate and other controlling measures. Further, on the basis of sensitivity analysis, the proposed model is restructured to obtained optimal control model by introducing time-dependent control variables for isolation, for vaccine efficacy and for treatment enhancement. Using optimal control theory and Pontryagin’s maximum principle, the model is optimized and important optimality conditions are derived. In order to explore the impact of various control measures on the disease dynamics, we considered three different scenarios, i.e., single and couple and threefold controlling interventions. Finally, the graphical interpretation of each case is depicted and discussed in detail. The simulation results revealed that although single and couple scenarios can be implemented for the disease minimization but, the effective case to curtail the disease incidence is the threefold scenario which implements all controlling measures at the same time.

Analysis of recovery cases of COVID19 of densely affected countries using LSTM deep learning model

“…Azimi et al [8] Estimate the reproduction of diseases affected. Exponential growth rate, maximum likelihood was evaluated.…”

“…So there may be discrepancies from the practical data. The work in [8] Covid-19 outbreak has been modeled mathematically by introducing Caputo Fractional derivatives. In [9] a compartmental model was made to formulate the epidemic.…”

Application of fractional optimal control theory for the mitigating of novel coronavirus in Algeria

“…In [9] , the authors investigated an optimal control problem couple with cost-effective analysis for the transmission dynamics of COVID-19. Recently, the role of some selected control measures including time dependent vaccine strategy on the incidence of COVID-19 is studied in [10] . Application of logistic modeling approach with a detail numerical analysis to explore the dynamical aspects of pandemic has been conducted in [11] .…”

Optimal control strategies to combat COVID-19 transmission: A mathematical model with incubation time delay

“…Right now, precautionary measures, government interventions, improved medical facilities, societal limitation on a huge scale, tracking of contacts, large-scale testing, identification and treatment of cases, face mask, sanitizer, etc., can be considered as useful and notable control strategies. Motivated by this some researchers [22] , [46] , [47] , [48] , [49] , [50] , [51] , [52] , [53] , [54] , [55] , [56] , [57] , [58] studied the optimal policies that could be employed to control COVID-19. Our goal is to study the outcome when we impose some restrictions on the susceptible class and provide medical help to infectious class.…”