An SVEIAR mumps infection model with vaccination and latent infection

JIANG Weiping; ZHANG Tailei; LIU Zongxuan; CAO Huan

doi:10.13471/j.cnki.acta.snus.ZR20240093

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An SVEIAR mumps infection model with vaccination and latent infection

Research articles | 更新时间：2025-11-14

- An SVEIAR mumps infection model with vaccination and latent infection
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 2, Pages: 148-159(2025)
- 作者机构：
  
  长安大学理学院，陕西西安 710064
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240093
  CLC： O175.1
- Received：01 April 2024，
  
  Accepted：28 May 2024，
  
  Published Online：28 August 2024，
  
  Published：15 March 2025
- 稿件说明：
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蒋为平,张太雷,刘宗萱等.一类具有疫苗接种且潜伏期传染的SVEIAR腮腺炎传染病模型[J].中山大学学报(自然科学版)(中英文),2025,64(02):148-159.

JIANG Weiping,ZHANG Tailei,LIU Zongxuan,et al.An SVEIAR mumps infection model with vaccination and latent infection[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(02):148-159.
蒋为平,张太雷,刘宗萱等.一类具有疫苗接种且潜伏期传染的SVEIAR腮腺炎传染病模型[J].中山大学学报(自然科学版)(中英文),2025,64(02):148-159. DOI： 10.13471/j.cnki.acta.snus.ZR20240093.

JIANG Weiping,ZHANG Tailei,LIU Zongxuan,et al.An SVEIAR mumps infection model with vaccination and latent infection[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(02):148-159. DOI： 10.13471/j.cnki.acta.snus.ZR20240093.

摘要

根据已知的腮腺炎传播机制，本文运用常微分方程定性与稳定性理论，建立了一类具有疫苗接种且潜伏期传染的SVEIAR腮腺炎传染病模型，得出了模型的基本再生数. 给出了平衡点的存在性并得到了当

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时，无病平衡点全局渐近稳定；当

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时，无病平衡点不稳定且地方病平衡点全局渐近稳定. 选取江苏省腮腺炎患者病例数据，应用模型模拟了腮腺炎未来几年的流行趋势.敏感性分析显示，疫苗接种是影响腮腺炎的非常重要的因素. 提高公众对腮腺炎的防范意识、制定有效的疫苗接种策略、加强锻炼能够提升机体素质以及免疫功能，从而预防腮腺炎的发生，进而控制腮腺炎的持续蔓延.

Abstract

According to the known mechanism of mumps transmission， a SVEIAR mumps infectious disease model with vaccination and incubation period was established by using the qualitative and stability theory of ordinary differential equation， and the basic regeneration number of the model was obtained. The existence of the equilibrium points is given and it is found that the disease-free equilibrium point is globally asymptotically stable when

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； the disease-free equilibrium point is unstable and the endemic equilibrium point is globally asymptotically stable when

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. The case data of mumps patients in Jiangsu Province is collected to simulate the epidemic trend of mumps in the next few years. Finally， the sensitivity analysis of parameters shows that the incidence of mumps will continue to increase in recent years. Improving public awareness preventing mumps， developing effective vaccination strategies and strengthening physical exercise can improve the body quality and immune function， so as to prevent the occurrence of mumps， and then control the spread of mumps.

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references

盖相臻， 2023 . 利用断点回归分析COVID-19疫情防控政策对济南地区儿童传染病发病及就诊趋势的影响［D］. 济南：山东大学 .

高文哲，雒志学， 2022 . 具有双接种的病毒变异传染病模型稳定性分析［J］. 重庆理工大学学报（自然科学）， 36 （ 11 ）： 266 - 273 .

康月月， 2020 . 两类多斑块下传染病模型的稳定性分析［D］. 兰州：兰州大学 .

马知恩，周义仓，李承治， 2015 . 常微分方程定性与稳定性方法［M］. 第二版，北京：科学出版社 .

殷秀岩，李丽娜， 2023 . 流行性腮腺炎的流行病学特征、发病趋势与防控措施［J］. 中国冶金工业医学杂志， 40 （ 2 ）： 189 - 190 .

ANDERSON R M ， CROMBIE J A ， GRENFELL B T ， 1987 . The epidemiology of mumps in the UK： A preliminary study of virus transmission， herd immunity and the potential impact of immunization ［J］. Epidemiol Infect ， 99 （ 1 ）： 65 - 84 .

ATTAULLAH A ， KHURSHAID A ， ZEESHAN Z ， et al ， 2022 . Computational framework of the SVIR epidemic model with a non-linear saturation incidence rate ［J］. Axioms ， 11 （ 11 ）： 651 .

BAI Y Z ， WANG X J ， GUO S B ， 2021 . Global stability of a mumps transmission model with quarantine measure ［J］. Acta Math Appl Sin ， 37 （ 4 ）： 665 - 672 .

DONAGHY M ， CAMERON J C ， FRIEDERICHS V ， 2006 . Increasing incidence of mumps in Scotland： Options for reducing transmission ［J］. J Clin Virol ， 35 （ 2 ）： 121 - 129 .

DURU E C ， ANYANWU M C ， 2023 . Mathematical model for the transmission of mumps and its optimal control ［J］. Biom Lett ， 60 （ 1 ）： 77 - 95 .

ECKALBAR J C ， ECKALBAR W L ， 2015 . Dynamics of an SIR model with vaccination dependent on past prevalence with high-order distributed delay ［J］. Biosystems ， 129 ： 50 - 65 .

FANOY E B ， CREMER J ， FERREIRA J A ， et al ， 2011 . Transmission of mumps virus from mumps-vaccinated individuals to close contacts ［J］. Vaccine ， 29 （ 51 ）： 9551 - 9556 .

FU X ， GE M ， XU W ， et al ， 2022 . Epidemiological features and sociodemographic factors associated with mumps in mainland China from 2004 to 2018 ［J］. J Med Virol ， 94 （ 10 ）： 4850 - 4859 .

LASALLE J P ， 1976 . The stability of dynamical systems ［M］. Berlin ： Hamilton Press .

MOHANA A ， BAR O ， PORAT BEN AMY D ， et al ， 2023 . Key findings and experience in the management of juvenile recurrent parotitis with sialoendoscopies—A retrospective study ［J］. Appl Sci ， 13 （ 19 ）： 10780 .

RUBIN S ， ECKHAUS M ， RENNICK L J ， et al ， 2015 . Molecular biology， pathogenesis and pathology of mumps virus ［J］. J Pathol ， 235 （ 2 ）： 242 - 252 .

SCHERER A ， McLEAN A ， 2002 . Mathematical models of vaccination ［J］. Br Med Bull ， 62 （ 1 ）： 187 - 199 .

SEPULVEDA G ， ARENAS A J ， GONZÁLEZ-PARRA G ， 2023 . Mathematical modeling of COVID-19 dynamics under two vaccination doses and delay effects ［J］. Mathematics ， 11 （ 2 ）： 369 .

SU S B ， CHANG H L ， CHEN A K ， 2020 . Current status of mumps virus infection： Epidemiology， pathogenesis， and vaccine ［J］. Int J Environ Res Public Health ， 17 （ 5 ）： 1686 .

van den DRIESSCHE P ， WATMOUGH J ， 2002 . Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission ［J］. Math Biosci ， 180 ： 29 - 48 .

VIJAYALAKSHMI G M ， ROSELYN B P , 2023 . Vaccination control measures of an epidemic model with long-term memristive effect ［J］. J Comput Appl Math ， 419 ： 114738 .

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