Optimal control strategies for a two-group epidemic model with vaccination-resource constraints

Zhang, Heting; Yang, Zhanwen; Pawelek, Kasia A.; Liu, Shengqiang

doi:10.1016/j.amc.2019.124956

Cited by 25 publications

(24 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been proved that all the subpopulations (and thus the total one) are nonnegative for all time so that the total population is also bounded for all time. us, one has from (5) that if b ≤ d, then one obtains from (5)…”

Section: Theoremmentioning

confidence: 99%

“…To prove Property (ii), assume that b > d. en, one has from (5) and the nonnegativity of the solution from eorem 1, since N(t) ≥ I(t), ∀t ∈ R 0+ , that…”

Section: Theoremmentioning

confidence: 99%

“…In this context, a relevant part of the available background literature has paid attention to their optimal management and application to the population. See, for instance, [1][2][3][4][5][6][7][8][9] and some of the references therein. On the other hand, it can be also pointed out that quarantine actions for the removal of some healthy susceptible individuals from the infective environment can be interpreted as an impulsive vaccination in continuous-time models, while a similar strategy on the infectious ones is in fact performed through an impulsive antiviral or antibiotic control.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls

Sen

Ibeas

Nistal

2021

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

This paper studies some basic properties of an SEIR (Susceptible-Exposed-Infectious-Recovered) epidemic model subject to vaccination and treatment controls. Firstly, the basic stability, boundedness, and nonnegativity of the state trajectory solution are investigated. Then, the problem of partial state reachability from a certain state value to a targeted one in finite time is focused on since it turns out that epidemic models are, because of their nature, neither (state) controllable from a given state to the origin nor reachable from a given initial condition. The particular formal statement of the partial reachability is focused on as a problem of output-reachability by defining a measurable output or lower dimension than that of the state. A special case of interest is that when the output is defined as the infectious subpopulation to be step-to-step tracked under suitable amounts being compatible with the required constraints. As a result, and provided that the output-controllability Gramian is nonsingular on a certain time interval of interest, a feedback control effort might be designed so that a prescribed value of the output can be approximately tracked. A linearization approximation is performed to simplify and facilitate the above task which is based on a point-to-point linearization of the solution trajectory. To this end, an “ad hoc” sampled approximate output trajectory is defined as control objective to be targeted through a point-wise calculated Jacobian matrix. A supervised appropriate restatement of the targeted suited sampled output values is redefined, if necessary, to make the initial proposed sampled trajectory compatible with the various needed constraints on nonnegativity and control boundedness. The design can be optionally performed under constant or adaptive sampling rates. Finally, some numerical examples are given to test the theoretical aspects and the design efficiency of the model.

show abstract

Section: Theoremmentioning

confidence: 99%

“…To prove Property (ii), assume that b > d. en, one has from (5) and the nonnegativity of the solution from eorem 1, since N(t) ≥ I(t), ∀t ∈ R 0+ , that…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls

Sen

Ibeas

Nistal

2021

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

“…The method used in the first category is mainly based on the method of random process, which usually uses the branching process of random process to explore the spread and evolution of infection population [1][2][3][4][5]. The second kind of method is mainly differential equation method, which is usually extended based on the compartmental model [6][7][8][9][10][11][12][13][14]. The third category mainly employs statistical physics methods, which usually consider disease -behavior interactions on complex networks [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…Ref. [10] established compartmental models for two different groups of people including high-risk and low-risk infection, and investigated the optimal allocation measures under different vaccinationresource constraints. In addition, a substantial complete review of coupling behavior and disease modeling based on statistical physical methods is given in Ref.…”

Section: Introductionmentioning

confidence: 99%

Infectious Disease Modeling and Epidemic Response Measures Analysis Considering Asymptomatic Infection

Chen

2020

IEEE Access

View full text Add to dashboard Cite

Classical SIR dynamic model and its derivative improved model may not accurately describe the epidemic situation similar to COVID-19 with characteristics of relative long incubation period and a large number of asymptomatic infections. Based on the existing epidemic compartment model, a novel compartment dynamic model considering actual transmission path of the symptomatic and asymptomatic infected is presented. Theoretical analysis and numerical simulation are employed to conduct prediction of development of the epidemic. According to different epidemic response measures, i.e., mitigation measures, suppression measures, medical treatment, evolutionary trend of epidemic situation under the initial population distribution structure are discussed. Results show that the control effects of different response measures on the number of deaths depend on the timing of the implementation of the measures. For mitigation response measures, the timing of the implementation of the measures has no obvious effect on the final epidemic, while for suppression response measures, the effect of suppression response measures in the early stage of the epidemic is significantly better than that in the middle and late stage of the epidemic development. Furthermore, no matter which stage the epidemic is in, the improvement of medical treatment level will play an important role in effectively reducing mortality. This study provides useful enlightenment and decision-making reference for policy makers to choose appropriate epidemic prevention and response measures in practice.

show abstract

Compartmental Modelling Approach for Accessing the Role of Non-Pharmaceutical Measures in the Spread of COVID-19

Bahri

Bhatia

Chauhan

et al. 2021

Mathematical Analysis for Transmission of COVID-19

View full text Add to dashboard Cite

Optimal control strategies for a two-group epidemic model with vaccination-resource constraints

Cited by 25 publications

References 37 publications

About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls

About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls

Infectious Disease Modeling and Epidemic Response Measures Analysis Considering Asymptomatic Infection

Compartmental Modelling Approach for Accessing the Role of Non-Pharmaceutical Measures in the Spread of COVID-19

Contact Info

Product

Resources

About