International Journal of Mathematics Trends and Technology
Volume 69 | Issue 8 | Year 2023 | Article Id. IJMTT-V69I8P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I8P511
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 23 Jun 2023 | 06 Aug 2023 | 20 Aug 2023 | 31 Aug 2023 |
Isolation is currently an effective measure to reduce exposure. In combination with this control factor, we take the isolation compartment into account in the infectious disease model. We build a system of SEIR with quarantine in the beginning. We calculate the basic reproduction number ℛ0 , which is the threshold for disease extinction. The disease-free equilibrium is globally asymptotically stable for ℛ0 <1, while is unstable for ℛ0 >1. Finally, we show that appropriate increasing the intensity of quarantine and vaccination coverage is effective for disease control numerically.
[1] Peng Zhou et al., “A Pneumonia Outbreak Associated with a New Coronavirus of Probable Bat Origin,” Nature, vol. 579, pp. 270-273, 2020.
[CrossRef ] [Google Scholar ] [Publisher Link ]
[2] Qun Li et al., “Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia,” New England Journal of Medicine, vol. 382, no. 13, pp. 1199-1207, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Fred Brauer, and Carlos Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Jia Li, and Zhien Ma, Dynamical Modeling and Analysis of Epidemics, World Scientific, Singapore, 2009.
[Google Scholar] [Publisher Link]
[5] Roy M. Anderson, and Robert M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.
[Google Scholar] [Publisher Link]
[6] Martin Nowak, and Robert M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, New York, 2000.
[Google Scholar] [Publisher Link]
[7] Anip Kumar Paul, and Md Abdul Kuddus, “Mathematical Analysis of a Covid-19 Model with Double Dose Vaccination in Bangladesh,” Results in Physics, vol. 35, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[8] Ramses Djidjou Demasse et al., “Optimal Control for an Age-Structured Model for the Transmission of Hepatitis B,” Journal of Mathematical Biology, vol. 73, no. 2, pp. 305-333, 2016.
[CrossRef] [Google Scholar ] [Publisher Link ]
[9] Juan Wang, Sha-Sha Gao, and Xue-Zhi Li, “A TB model with Infectivity in Latent Period and Imperfect Treatment,” Discrete Dynamics in Nature and Society, pp. 1-19, 2012.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Zhong-Kai Guo, Hai-Feng Huo, and Hong Xiang, “Global Dynamics of an Age-Structured Malaria Model with Prevention,” Mathematical Biosciences and Engineering, vol. 16, no. 3, pp. 1625-1653, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[11] C. Connell McCluskey, “Global Stability for an SEI Model of Infectious Disease with Age Structure and Immigration of Infecteds,” Mathematical Biosciences and Engineering, vol. 13, no. 2, pp. 381-400, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[12] Joshua Kiddy K. Asamoah et al., “Sensitivity Assessment and Optimal Economic Evaluation of a New Covid-19 Compartmental Epidemic Model with Control Interventions,” Chaos Solitons and Fractals, vol. 146, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[13] Areej Alshorman et al., “An HIV Model with Age-Structured Latently Infected Cells,” Journal of Biological Dynamics, vol. 11, pp. 192-215, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Tianyi Qiu, Han Xiao, and Vladimir Brusic, “Estimating the Effects of Public Health Measures by SEIR(MH) Model Of Covid-19 Epidemic in Local Geographic Areas,” Frontiers in Public Health, vol. 9, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[15] Maoxing Liu, and Yuming Chen, “An SIRS Model with Differential Susceptibility and Infectivity on Uncorrelated Networks,” Mathematical Biosciences and Engineering, vol. 12, no. 3, pp. 415-429, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[16] V. Skakauskas, “The Kermack-McKendrick Epidemic Model with Variable Infectivity Modified,” Journal of Mathematical Analysis and Applications, vol. 507, no. 2, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Jean Pierre II Kouenkam, Joseph Mbang, and Yves Emvudu, “Global Dynamics of a Model of Hepatitis B Virus Infection in a Sub-Saharan African Rural Area,” International Journal of Biomathematics, vol. 13, no. 6, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[18] Xiaogang Liu et al., “Global Stability of Latency-Age/Stage-Structured Epidemic Models With Differential Infectivity,” Journal of Mathematical Biology, vol. 86, no. 80, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[19] Herbert W. Hethcote, and Simon A. Levin, “Periodicity in Epidemiological Models,” Applied Mathematical Ecology, vol. 18, pp. 193- 211, 1989.
[CrossRef [Google Scholar] [Publisher Link]
[20] Nicolas Bacaër, and Souad Guernaoui, “The Epidemic Threshold of Vector-Borne Diseases with Seasonality,” Journal of Mathematical Biology, vol. 53, no. 3, pp. 421-436, 2006.
[CrossRef] [Google Scholar] [Publisher Link]
[21] David J. D. Earn et al., “A Simple Model for Complex Dynamical Transitions in Epidemics,” Science, vol. 287, no. 5453, pp. 667-670, 2000.
[CrossRef] [Google Scholar] [Publisher Link]
[22] Jicai Huang et al., “Seasonal Transmission Dynamics of Measles in China,” Theory in Biosciences, vol. 137, no. 2, pp. 185-195, 2018.
[CrossRef] [Google Scholar] [Publisher Link]
[23] Wendi Wang, and Xiao-Qiang Zhao, “Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments,” Journal of Dynamics and Differential Equations, vol. 20, no. 3, pp. 699-717, 2008.
[CrossRef [Google Scholar] [Publisher Link]
[24] Fang Zhang, and Xiao-Qiang Zhao, “A Periodic Epidemic Model in a Patchy Environment,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 496-516, 2007.
[CrossRef] [Google Scholar] [Publisher Link]
[25] Horst R. Thieme, “Convergence Results and a Poincar-Bendixson Trichotomy for Asymptotically Autonomous Differential Equations,” Journal of Mathematical Biology, vol. 30, pp. 755-763, 1992.
[CrossRef] [Google Scholar] [Publisher Link ]
[26] Lawrence Perko, Differential Equations and Dynamical Systems, 3rd edition, Springer, New York, 2013.
[Google Scholar] [Publisher Link]
[27] Xiao-Qiang Zhao, Dynamical Systems in Population Biology, Springer, New York, 2007.
[CrossRef] [Google Scholar] [Publisher Link]
[28] Andrei Korobeinikov, “Global Properties of Basic Virus Dynamics Models,” Bulletin of Mathematical Biology, vol. 66, no. 4, pp. 879- 883, 2004.
[CrossRef ] [Google Scholar] [Publisher Link]
[29] Jianquan Li, Yali Yang, and Yicang Zhou, “Global Stability of an Epidemic Model with Latent Stage and Vaccination,” Nonlinear Analysis-Real World Applications, vol. 12, no. 4, pp. 2163-2173, 2011.
[CrossRef] [Google Scholar] [Publisher Link]
Yajing Shen, "Global Stability of SEIQR Model with Isolation Compartment," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 8, pp. 87-92, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I8P511
PDF 
Abstract 
Keywords 
References 
Citation