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

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 helpfu...

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Main Authors: Bing Li, Ziye Xiang
Format: Article
Language:English
Published: MDPI AG 2023-06-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/11/12/2697
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author Bing Li
Ziye Xiang
author_facet Bing Li
Ziye Xiang
author_sort Bing Li
collection DOAJ
description 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>I</mi><msub><mi>V</mi><mi>A</mi></msub><msub><mi>V</mi><mi>B</mi></msub><mi>R</mi></mrow></semantics></math></inline-formula>) 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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spelling doaj.art-2c8dfd942ad549d39eefdf39b8e628532023-11-18T11:28:33ZengMDPI AGMathematics2227-73902023-06-011112269710.3390/math11122697Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex NodesBing Li0Ziye Xiang1School of Economics, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Economics, Wuhan University of Technology, Wuhan 430070, ChinaVaccines 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>I</mi><msub><mi>V</mi><mi>A</mi></msub><msub><mi>V</mi><mi>B</mi></msub><mi>R</mi></mrow></semantics></math></inline-formula>) 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.https://www.mdpi.com/2227-7390/11/12/2697epidemic spread dynamicscomplex networksevolutionary gamevaccination
spellingShingle Bing Li
Ziye Xiang
Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes
Mathematics
epidemic spread dynamics
complex networks
evolutionary game
vaccination
title Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes
title_full Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes
title_fullStr Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes
title_full_unstemmed Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes
title_short Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes
title_sort evolutionary game of vaccination considering both epidemic and economic factors by infectious network of complex nodes
topic epidemic spread dynamics
complex networks
evolutionary game
vaccination
url https://www.mdpi.com/2227-7390/11/12/2697
work_keys_str_mv AT bingli evolutionarygameofvaccinationconsideringbothepidemicandeconomicfactorsbyinfectiousnetworkofcomplexnodes
AT ziyexiang evolutionarygameofvaccinationconsideringbothepidemicandeconomicfactorsbyinfectiousnetworkofcomplexnodes