Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Ma, Yanli; Liu, Jia‐Bao; Li, Haixia

doi:10.3390/math6120328

Cited by 28 publications

(17 citation statements)

References 28 publications

(32 reference statements)

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“…The unidentified infected are defined as the infected but not identified people who are not yet isolated and can transmit the disease to the susceptible. In addition to the SUC model, various mathematical models for infectious diseases have been studied [ 21 , 22 , 23 , 24 , 25 , 26 ]. Nevertheless, we use the SUC model to consider the unconfirmed infections for controlling the highly contagious COVID-19 more effectively.…”

Section: Introductionmentioning

confidence: 99%

Controlling COVID-19 Outbreaks with Financial Incentives

Lee

Kwak

Kim

2021

IJERPH

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In this paper, we consider controlling coronavirus disease 2019 (COVID-19) outbreaks with financial incentives. We use the recently developed susceptible-unidentified infected-confirmed (SUC) epidemic model. The unidentified infected population is defined as the infected people who are not yet identified and isolated and can spread the disease to susceptible individuals. It is important to quickly identify and isolate infected people among the unidentified infected population to prevent the infectious disease from spreading. Considering financial incentives as a strategy to control the spread of disease, we predict the effect of the strategy through a mathematical model. Although incentive costs are required, the duration of the disease can be shortened. First, we estimate the unidentified infected cases of COVID-19 in South Korea using the SUC model, and compute two parameters such as the disease transmission rate and the inverse of the average time for confirming infected individuals. We assume that when financial incentives are provided, there are changes in the proportion of confirmed patients out of unidentified infected people in the SUC model. We evaluate the numbers of confirmed and unidentified infected cases with respect to one parameter while fixing the other estimated parameters. We investigate the effect of the incentives on the termination time of the spread of the disease. The larger the incentive budget is, the faster the epidemic will end. Therefore, financial incentives can have the advantage of reducing the total cost required to prevent the spread of the disease, treat confirmed patients, and recover overall economic losses.

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Section: Introductionmentioning

confidence: 99%

Controlling COVID-19 Outbreaks with Financial Incentives

Lee

Kwak

Kim

2021

IJERPH

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“…For example, without an effective vaccine, the rapid spread of coronavirus disease 2019 (COVID-19) worldwide has had a serious socioeconomic impact and imposed a potentially great threat to human safety [14]. Hence, many suitable SIQR epidemic models have been developed in the past few decades [15][16][17][18][19]. In [15], Herbert and Ma obtained the corresponding basic reproduction number of a deterministic SIQR model with quarantineadjusted incidence.…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity

et al. 2021

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Recently, considering the temporary immunity of individuals who have recovered from certain infectious diseases, Liu et al. (Phys A Stat Mech Appl 551:124152, 2020 ) proposed and studied a stochastic susceptible-infected-recovered-susceptible model with logistic growth. For a more realistic situation, the effects of quarantine strategies and stochasticity should be taken into account. Hence, our paper focuses on a stochastic susceptible-infected-quarantined-recovered-susceptible epidemic model with temporary immunity. First, by means of the Khas’minskii theory and Lyapunov function approach, we construct a critical value corresponding to the basic reproduction number of the deterministic system. Moreover, we prove that there is a unique ergodic stationary distribution if . Focusing on the results of Zhou et al. (Chaos Soliton Fractals 137:109865, 2020), we develop some suitable solving theories for the general four-dimensional Fokker–Planck equation. The key aim of the present study is to obtain the explicit density function expression of the stationary distribution under . It should be noted that the existence of an ergodic stationary distribution together with the unique exact probability density function can reveal all the dynamical properties of disease persistence in both epidemiological and statistical aspects. Next, some numerical simulations together with parameter analyses are shown to support our theoretical results. Last, through comparison with other articles, results are discussed and the main conclusions are highlighted.

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“…Investigation of the global stability of endemic equilibrium in the mathematical model of infectious diseases is one of the important issues in epidemiology [12][13][14][15][16][17][18][19][20]. Several methods have been proposed by researchers to prove the stability of equilibrium points, such as monotone dynamical systems, the geometric approach, and the method of Lyapunov functions [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

An Approach for the Global Stability of Mathematical Model of an Infectious Disease

et al. 2020

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The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

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Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Cited by 28 publications

References 28 publications

Controlling COVID-19 Outbreaks with Financial Incentives

Controlling COVID-19 Outbreaks with Financial Incentives

Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity

An Approach for the Global Stability of Mathematical Model of an Infectious Disease

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