Control of a multigroup COVID-19 model with immunity: treatment and test elimination

Abstract

This paper introduces a multigroup COVID-19 model with immunity, in which the total population of each group is partitioned into five compartments, that is, susceptible, exposed, infective, infective in treatment and recovered compartment. If the basic reproduction number is less than or equal to one, and the infection graph is strongly connected, then the disease-free equilibrium is globally asymptotically stable and the disease dies out. However, the COVID-19 is already in a pandemic state, and the basic reproduction number is large than one. Hence, in order to make the COVID-19 die out in some groups in an area, we design some appropriate control strategies which reduce the number of exposed people and increase the number of people treated. These two methods have been proved to be the most effective methods at present. An effective algorithm is proposed to identify the groups that need to be controlled. Finally, we use the actual limited data of Hubei, Guangdong and Zhejiang provinces in China to illustrate the effectiveness of the obtained results.

On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible

“…Therefore, discrete epidemic models have been found appropriate for processing such data. See, for instance, [ 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 ] and some related references therein. Studies on particular data for different countries or regions can be found in the literature related to COVID-19, sometimes related to public interventions, such as quarantines, isolation measures, lockdowns, use of masks, social distance rules, etc.…”

“…Such a model includes three different infectious subpopulations, namely, the slightly infections, the hospitalized ones and the ones staying at the intensive care units are considered. On the other hand, the implementation of control rules oriented either toward reducing the number of exposed individuals or toward increasing the number of treated individuals is proposed and discussed in [ 20 ] while impulsive optimal control techniques are developed in [ 21 ]. In particular, the analysis technique proposed in [ 20 ] relies on the fact that the epidemics is endemic.…”

“…On the other hand, the implementation of control rules oriented either toward reducing the number of exposed individuals or toward increasing the number of treated individuals is proposed and discussed in [ 20 ] while impulsive optimal control techniques are developed in [ 21 ]. In particular, the analysis technique proposed in [ 20 ] relies on the fact that the epidemics is endemic. In [ 23 ], the inadequacy of the implementation of open-loop (i.e., without using feedback) controls is emphasized contrarily to the use of closed-loop controls like, for instance, sliding mode-based control or other feedback laws.…”

On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

“…Each one of the above subpopulations as well as the asymptomatic ones have their own transitions from the exposed subpopulation, and vaccination and treatment controls are also considered to satisfy a priori established hospitalization constraints for the seriously infectious individuals on availability of beds and specific needed hospital means for intensive treatment. On the other hand, the implementation of control strategies oriented to reduce the number of exposed individuals or to increase the number of treated individuals is proposed and discussed in [20], while impulsive optimal control techniques are developed in [21]. In particular, the proposal of [20] relies on the fact that the pandemic is now endemic.…”

“…On the other hand, the implementation of control strategies oriented to reduce the number of exposed individuals or to increase the number of treated individuals is proposed and discussed in [20], while impulsive optimal control techniques are developed in [21]. In particular, the proposal of [20] relies on the fact that the pandemic is now endemic. In [23], the inadequacy of open-loop controls is emphasized in contrast to closed-loop controls like, for instance, sliding mode-based control laws.…”