An SEQAIHR model to study COVID-19 transmission and optimal control strategies in Hong Kong, 2022

Abstract

During the COVID-19 pandemic, one of the major concerns was a medical emergency in human society. Therefore it was necessary to control or restrict the disease spreading among populations in any fruitful way at that time. To frame out a proper policy for controlling COVID-19 spreading with limited medical facilities, here we propose an SEQAIHR model having saturated treatment. We check biological feasibility of model solutions and compute the basic reproduction number ( ). Moreover, the model exhibits transcritical, backward bifurcation and forward bifurcation with hysteresis with respect to different parameters under some restrictions. Further to validate the model, we fit it with real COVID-19 infected data of Hong Kong from 19th December, 2021 to 3rd April, 2022 and estimate model parameters. Applying sensitivity analysis, we find out the most sensitive parameters that have an effect on . We estimate using actual initial growth data of COVID-19 and calculate effective reproduction number for same period. Finally, an optimal control problem has been proposed considering effective vaccination and saturated treatment for hospitalized class to decrease density of the infected class and to minimize implemented cost.

Transmission Dynamics of COVID-19 with Saturated Treatment: A Case Study of Spain

“…This type of phenomenon occurs due to the presence of saturated treatment. In [13,14,18], we see that the infected being delayed for treatment is one of the origins that lead to the backward bifurcation. But the consideration of linear treatment function does not ensure the phenomenon of backward bifurcation [11,19,20].…”

“…An ODE compartmental model with saturated treatment due to the limited medical facilities such as lack of hospital beds and oxygen cylinder, in Italy, was studied to drag down the spread of COVID-19, where the prescribed model determines the scenario of COVID-19 handled by maintaining a lockdown [13]. A study for COVID-19 transmission and its control in Hong Kong is discussed in [14].…”

Mathematical Analysis of Fractal-Fractional Mathematical Model of COVID-19

“…R0 is estimated using actual initial growth data of COVID-19, and the effective reproduction number is calculated for the same period. Finally, an optimal control problem is proposed, taking into account effective vaccination and saturated treatment for the hospitalized class, to reduce the density of the infected class and minimize the implemented cost [3].…”

A brief discussion about a predator-prey model including disease in predators with the delay effect

“…Understanding the evolution and dynamics of infectious diseases is crucial for preventing, controlling, and eradicating such diseases in any biological community. In [21,1,14,16,28,31,41,42], authors explore the dynamics of infectious disease with the combined effect of epidemiological and demographic factors simultaneously on an ecological population. The first mathematical model of an infectious disease in a population was introduced by Kermack and McKendrick [21].…”

“…In 2001, Han et al [14] studied the modifications of several predator-prey models involving SIS or SIR infection. Saha et al [42] have discussed a SEQAIHR model for analyzing COVID-19 transmission and optimal control strategies. Another significant research area that deals with disease transmission in the population models, it is known as Ecoepidemiology.…”