Dynamics analysis and optimal control of SIVR epidemic model with incomplete immunity

Liu, Yiming; Jian, Shuang; Gao, Jianguo

doi:10.1186/s13662-022-03723-7

Cited by 7 publications

(6 citation statements)

References 26 publications

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“…To compute the optimal vaccination strategy that would minimize infected individuals and minimize the vaccine factors, we consider the optimal control problem [ 47 , 48 , 49 , 50 ] as

…”

Section: Statement Of the Optimal Control Problemmentioning

confidence: 99%

“…Equations (1)–(4) and belonging to a set of acceptable controls,

where,

. The term

represents the weighted costs involved with using control

and

defined to denote the weight coefficient of the susceptible individuals [ 47 , 48 , 49 , 50 ].…”

Section: Statement Of the Optimal Control Problemmentioning

confidence: 99%

“…Here, the transversality conditions [ 47 , 48 , 49 , 50 ] are

and

. The Hamiltonian function H and

is strongly convex.…”

Section: Statement Of the Optimal Control Problemmentioning

confidence: 99%

See 2 more Smart Citations

Understanding the Impact of Vaccination and Self-Defense Measures on Epidemic Dynamics Using an Embedded Optimization and Evolutionary Game Theory Methodology

Kabir,

Islam,

Sharif Ullah

2023

Vaccines

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Explaining how individual choice and government policy can appear in the same context in real society is one of the most challenging scientific problems. Controlling infectious diseases requires effective prevention and control measures, including vaccination and self-defense measures. In this context, optimal control strategies incorporating vaccination and self-defense measures have been proposed using the framework of evolutionary game theory. This approach accounts for individuals’ behavior and interactions in a population. It can provide insights into the effectiveness of different strategies for controlling the spread of infectious diseases. The optimal control strategy involves balancing the costs and benefits of vaccination, considering the dynamic interplay between the infected and susceptible populations. By combining evolutionary game theory with optimal control theory, we can identify the optimal allocation of resources for vaccination and self-defense measures, which can maximize the control of infectious diseases while minimizing costs. The model is utilized to analyze public health policies diseases, such as vaccination and self-defense strategies, to mitigate the spread of infectious in the context of delayed decision-making.

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“…To compute the optimal vaccination strategy that would minimize infected individuals and minimize the vaccine factors, we consider the optimal control problem [ 47 , 48 , 49 , 50 ] as

…”

Section: Statement Of the Optimal Control Problemmentioning

confidence: 99%

“…Equations (1)–(4) and belonging to a set of acceptable controls,

where,

. The term

represents the weighted costs involved with using control

and

defined to denote the weight coefficient of the susceptible individuals [ 47 , 48 , 49 , 50 ].…”

Section: Statement Of the Optimal Control Problemmentioning

confidence: 99%

See 1 more Smart Citation

Understanding the Impact of Vaccination and Self-Defense Measures on Epidemic Dynamics Using an Embedded Optimization and Evolutionary Game Theory Methodology

Kabir,

Islam,

Sharif Ullah

2023

Vaccines

View full text Add to dashboard Cite

show abstract

“…Moreover, some physical systems such as the visco-elastic damper model [33] were analyzed with FDEs. Other than this, the theory of periodic reactions [34] and the advanced analysis of SIVR models [35,36] have also paved a path on which our timedependent disease model can proceed.…”

Section: Motivation and State Of The Artmentioning

confidence: 99%

On a Novel Dynamics of a SIVR Model Using a Laplace Adomian Decomposition Based on a Vaccination Strategy

Dhandapani¹,

Leiva

Martín-Barreiro

et al. 2023

Fractal Fract

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In this paper, we introduce a SIVR model using the Laplace Adomian decomposition. This model focuses on a new trend in mathematical epidemiology dedicated to studying the characteristics of vaccination of infected communities. We analyze the epidemiological parameters using equilibrium stability and numerical analysis techniques. New mathematical strategies are also applied to establish our epidemic model, which is a pandemic model as well. In addition, we mathematically establish the chance for the next wave of any pandemic disease and show that a consistent vaccination strategy could control it. Our proposal is the first model introducing a vaccination strategy to actively infected cases. We are sure this work will serve as the basis for future research on COVID-19 and pandemic diseases since our study also considers the vaccinated population.

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“…[18,19]. Based on the SIR model, the SIVR (Susceptible-Infected-Vaccinated-Recovered) model is defined by the vaccinated individuals [20]. This model has been widely used by scholars because the combination of the pandemic process with effective prevention decisions can be evaluated.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes

Xiang

2023

Mathematics

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Vaccines are recognized as an effective way to control the spread of epidemics. It should be noted that the vaccination of a population is influenced not only by the infectiousness of a disease but also the vaccination strategy, such as the cost of vaccination. An accurate prediction model is helpful in forecasting the most likely trend to support smart decisions. In order to solve this problem, a model of epidemic spread dynamics is proposed, which is called the Susceptible–Infected–Vaccinated with vaccine A–Vaccinated with vaccine B–Recovered (SIVAVBR) model. This model assesses the competition between two vaccines in terms of economic cost and protection effectiveness in an open-market economy. The optimization process of individual vaccination decision-making was studied in an evolutionary game. In addition, a novel network containing environmental nodes and individual nodes was used to simulate the increase in infection probability caused by aggregation. Using the mean-field approach, the existence and stability of the disease-free equilibrium point and the endemic equilibrium point were demonstrated. Numerous simulations were further carried out to examine the relationship between the basic reproduction number and epidemic dynamics. The results reveal that immunization hesitation reduces the immunity level of the entire population. It is important to improve vaccine efficiency and affordability for manufacturers to become more competitive. Establishing the core individuals in the network is also a means of quickly occupying the market.

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Dynamics analysis and optimal control of SIVR epidemic model with incomplete immunity

Cited by 7 publications

References 26 publications

Understanding the Impact of Vaccination and Self-Defense Measures on Epidemic Dynamics Using an Embedded Optimization and Evolutionary Game Theory Methodology

Understanding the Impact of Vaccination and Self-Defense Measures on Epidemic Dynamics Using an Embedded Optimization and Evolutionary Game Theory Methodology

On a Novel Dynamics of a SIVR Model Using a Laplace Adomian Decomposition Based on a Vaccination Strategy

Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes

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