Search Advanced

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 3: 3742-3754. doi: 10.3934/mbe.2024165
Previous Article Next Article
Research article Special Issues

Drawing a parallel between the trend of confirmed COVID-19 deaths in the winters of 2022/2023 and 2023/2024 in Italy, with a prediction

  • Department of Computer Science and Engineering, University of Bologna, Bologna, Italy

  • We studied the weekly number and the growth/decline rates of COVID-19 deaths of the period from October 31, 2022, to February 9, 2023, in Italy. We found that the COVID-19 winter wave reached its peak during the three holiday weeks from December 16, 2022, to January 5, 2023, and it was definitely trending downward, returning to the same number of deaths as the end of October 2022, in the first week February 2023. During this period of 15 weeks, that wave caused a number of deaths as large as 8,526. Its average growth rate was +7.89% deaths per week (10 weeks), while the average weekly decline rate was -15.85% (5 weeks). At the time of writing of this paper, Italy has been experiencing a new COVID-19 wave, with the latest 7 weekly bulletins (October 26, 2023 – December 13, 2023) showing that deaths have climbed from 148 to 322. The weekly growth rate had risen by +14.08% deaths, on average. Hypothesizing that this 2023/2024 wave will have a total duration similar to that of 2022/2023, with comparable extensions of both the growth period and the decline period and similar growth/decline rates, we predict that the number of COVID-19 deaths of the period from the end of October 2023 to the beginning of February 2024 should be less than 4100. A preliminary assessment of this forecast, based on 11 of the 15 weeks of the period, has already confirmed the accuracy of this approach.

    Citation: Marco Roccetti. Drawing a parallel between the trend of confirmed COVID-19 deaths in the winters of 2022/2023 and 2023/2024 in Italy, with a prediction[J]. Mathematical Biosciences and Engineering, 2024, 21(3): 3742-3754. doi: 10.3934/mbe.2024165

    Related Papers:

    [1] Hai-Feng Huo, Qian Yang, Hong Xiang . Dynamics of an edge-based SEIR model for sexually transmitted diseases. Mathematical Biosciences and Engineering, 2020, 17(1): 669-699. doi: 10.3934/mbe.2020035
    [2] Jianquan Li, Yiqun Li, Yali Yang . Epidemic characteristics of two classic models and the dependence on the initial conditions. Mathematical Biosciences and Engineering, 2016, 13(5): 999-1010. doi: 10.3934/mbe.2016027
    [3] Yu Tsubouchi, Yasuhiro Takeuchi, Shinji Nakaoka . Calculation of final size for vector-transmitted epidemic model. Mathematical Biosciences and Engineering, 2019, 16(4): 2219-2232. doi: 10.3934/mbe.2019109
    [4] Fred Brauer . Age-of-infection and the final size relation. Mathematical Biosciences and Engineering, 2008, 5(4): 681-690. doi: 10.3934/mbe.2008.5.681
    [5] Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman . The basic reproduction number R0 and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1455-1474. doi: 10.3934/mbe.2013.10.1455
    [6] Julijana Gjorgjieva, Kelly Smith, Gerardo Chowell, Fabio Sánchez, Jessica Snyder, Carlos Castillo-Chavez . The Role of Vaccination in the Control of SARS. Mathematical Biosciences and Engineering, 2005, 2(4): 753-769. doi: 10.3934/mbe.2005.2.753
    [7] Z. Feng . Final and peak epidemic sizes for SEIR models with quarantine and isolation. Mathematical Biosciences and Engineering, 2007, 4(4): 675-686. doi: 10.3934/mbe.2007.4.675
    [8] Sarafa A. Iyaniwura, Musa Rabiu, Jummy F. David, Jude D. Kong . Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study. Mathematical Biosciences and Engineering, 2021, 18(6): 8905-8932. doi: 10.3934/mbe.2021439
    [9] Jinlong Lv, Songbai Guo, Jing-An Cui, Jianjun Paul Tian . Asymptomatic transmission shifts epidemic dynamics. Mathematical Biosciences and Engineering, 2021, 18(1): 92-111. doi: 10.3934/mbe.2021005
    [10] Fred Brauer, Zhisheng Shuai, P. van den Driessche . Dynamics of an age-of-infection cholera model. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1335-1349. doi: 10.3934/mbe.2013.10.1335

  • We studied the weekly number and the growth/decline rates of COVID-19 deaths of the period from October 31, 2022, to February 9, 2023, in Italy. We found that the COVID-19 winter wave reached its peak during the three holiday weeks from December 16, 2022, to January 5, 2023, and it was definitely trending downward, returning to the same number of deaths as the end of October 2022, in the first week February 2023. During this period of 15 weeks, that wave caused a number of deaths as large as 8,526. Its average growth rate was +7.89% deaths per week (10 weeks), while the average weekly decline rate was -15.85% (5 weeks). At the time of writing of this paper, Italy has been experiencing a new COVID-19 wave, with the latest 7 weekly bulletins (October 26, 2023 – December 13, 2023) showing that deaths have climbed from 148 to 322. The weekly growth rate had risen by +14.08% deaths, on average. Hypothesizing that this 2023/2024 wave will have a total duration similar to that of 2022/2023, with comparable extensions of both the growth period and the decline period and similar growth/decline rates, we predict that the number of COVID-19 deaths of the period from the end of October 2023 to the beginning of February 2024 should be less than 4100. A preliminary assessment of this forecast, based on 11 of the 15 weeks of the period, has already confirmed the accuracy of this approach.




    [1] L. Casini, M, Roccetti, Reopening Italy's schools in September 2020: A Bayesian estimation of the change in the growth rate of new SARSCoV-2 cases, BMJ Open, 11 (2021), 1–7. https://doi.org/10.1136/bmjopen-2021-051458 doi: 10.1136/bmjopen-2021-051458
    [2] C. Liu, J. Huang, S. Chen, D. Wang, L. Zhang, X. Liu, X. Lian, The impact of crowd gatherings on the spread of COVID-19, Environ. Res., 213 (2022), 1–8. https://doi.org/10.1016/j.envres.2022.113604 doi: 10.1016/j.envres.2022.113604
    [3] R. Cappi, L. Casini, D. Tosi, M. Roccetti. Questioning the seasonality of SARS-COV-2: A Fourier spectral analysis, BMJ Open, 12 (2022), 1–12. https://doi.org/10.1136/bmjopen-2022-061602 doi: 10.1136/bmjopen-2022-061602
    [4] Italian Ministry of Health. Weekly Bulletins—COVID-19. Available from: https://www.salute.gov.it/portale/nuovocoronavirus/archivioBollettiniNuovoCoronavirus.jsp (accessed on 15 December 2023).
    [5] E. Mathieu, H. Ritchie, L. Rodés Guirao, C. Appel, D. Gavrilov, C. Giattino, et al., Coronavirus (COVID-19) Deaths, 2023. Available from: https://ourworldindata.org/covid-deaths (accessed on 15 December 2023).
    [6] C. El Aoun, H. Eleuch, H. Ben Ayed, E. Aïmeur, F. Kamun, Analogy in Making Predictions, J. Decis. Syst., 16 (2007), 393–416. https://doi.org/10.3166/jds.16.393-416 doi: 10.3166/jds.16.393-416
    [7] M. Bar, The proactive brain: using analogies and associations to generate predictions, Trends Cogn. Sci., 11 (2007), 280–289. https://doi.org/10.1016/j.tics.2007.05.005 doi: 10.1016/j.tics.2007.05.005
    [8] I. Cooper, A. Mondal, C.G. Antonopoulos, A SIR model assumption for the spread of COVID-19 in different communities, Chaos Solit. Fractals, 139 (2020), 1–14. https://doi.org/10.1016/j.chaos.2020.110057 doi: 10.1016/j.chaos.2020.110057
    [9] M. Gaspari, The impact of test positivity on surveillance with asymptomatic carriers, Epidemiol. Methods, 11 (2022). https://doi.org/10.1515/em-2022-0125 doi: 10.1515/em-2022-0125
    [10] M. Roccetti, Excess mortality and COVID-19 deaths in Italy: A peak comparison study, Math. Biosci. Eng., 20 (2023), 7042–7055. https://doi.org/10.3934/mbe.2023304 doi: 10.3934/mbe.2023304
    [11] S. Piconi, S. Pontiggia, M. Franzetti, F. Branda, D.Tosi, Statistical models to predict clinical outcomes with anakinra vs. tocilizumab treatments for severe pneumonia in COVID19 patients, Eur. J. Intern. Med., 112 (2023), 118–120. https://doi.org/10.1016/j.ejim.2023.01.024 doi: 10.1016/j.ejim.2023.01.024
    [12] D. Tosi, A. Campi, How schools affected the COVID-19 pandemic in Italy: Data analysis for Lombardy Region, Campania Region and Emilia Region, Future Internet, 13 (2021), 1–12. https://doi.org/10.3390/fi13050109 doi: 10.3390/fi13050109
    [13] D. Tosi, A. Campi, How data analytics and Big Data can help scientists in managing COVID-19 diffusion: A model to predict the COVID-19 diffusion in Italy and Lombardy Region, J. Med. Internet Res., 22 (2020), 1–21, https://doi.org/10.2196/21081 doi: 10.2196/21081
    [14] D. Tosi, A. Verde, M. Verde, Clarification of misleading perceptions of COVID-19 fatality and testing rates in Italy: Data analysis, J. Med. Internet Res., 22 (2020), 1–14. https://doi.org/10.2196/19825 doi: 10.2196/19825
    [15] Italian RAI Broadcaster, RAINews. Weekly Bullettins COVID-19. Available from: https://www.rainews.it/ran24/speciali/2020/covid19/ (accessed on 15 December 2023).
    [16] K. C. Greene, S. Armstrong, J. Scott, Structured analogies for forecasting. Int. J. Forecast., 23 (2007), 365–376. https://doi.org/10.1016/j.ijforecast.2007.05.005 doi: 10.1016/j.ijforecast.2007.05.005
    [17] P. Nasa, R. Jain, D. Juneja, Delphi methodology in healthcare research: How to decide its appropriateness, World J. Methodol., 11 (2021), 116–129. https://doi.org/10.5662/wjm.v11.i4.116 doi: 10.5662/wjm.v11.i4.116
    [18] P. Salomoni, S. Mirri, S. Ferretti, M. Roccetti, Profiling learners with special needs for custom e-learning experiences, a closed case?, ACM Int. Conf. Proceed. Ser., 225 (2007), 84–92. https://doi.org/10.1145/1243441.1243462 doi: 10.1145/1243441.1243462
    [19] S-P. Jun, T-E. Sung, H-W Park, Forecasting by analogy using the web search traffic, Technol. Forecasting Soc. Change, 115 (2017), 37–51, https://doi.org/10.1016/j.techfore.2016.09.014 doi: 10.1016/j.techfore.2016.09.014
    [20] Italian Ministry of Health. Vaccinations 2023/2024 – COVID-19. Available from: https://www.governo.it/it/cscovid19/report-vaccini/ (accessed on 15 December 2023).
    [21] C. Mattiuzzi, G. Lippi, Update on the status of COVID-19 vaccination in Italy - April 2023. Immunol. Res., 71 (2023), 671–672. https://doi.org/10.1007/s12026-023-09383-3 doi: 10.1007/s12026-023-09383-3
    [22] K. Katella, Omicron, Delta, Alpha, and More: What to know about the Coronavirus variants, Yale Medicine, 2023. Available from: https://www.yalemedicine.org/news/covid-19-variants-of-concern-omicron (accessed on 15 December 2023).
    [23] F. Baum T. Freeman, C. Musolino, M. Abramovitz, W. De Ceukelaire, J. Flavel, et al., Explaining covid-19 performance: What factors might predict national responses? BMJ, 372 (2021). https://doi.org/10.1136/bmj.n91 doi: 10.1136/bmj.n91
    [24] I. Ciufolini, A. Paolozzi, An improved mathematical prediction of the time evolution of the Covid-19 pandemic in Italy, with a Monte Carlo simulation and error analyses, Eur. Phys. J. Plus, 135 (2020), 1–13. https://doi.org/10.1140/epjp/s13360-020-00488-4 doi: 10.1140/epjp/s13360-020-00488-4
    [25] Italian Historical Video Archive - Istituto Luce. Flu Epidemic in Italy, 1969–1970. Available from: https://www.raiplay.it/video/2020/03/Frontiere---Coronavirus-Asiatica-del-1969-In-Italia-5000-morti-e-13-milioni-a-letto-d93814e9-3b14-4e5c-8b41-e0eaa87f7cd0.html (accessed on 15 December 2023).
    [26] C. Rizzo, A. Bella, C. Viboud, L. Simonsen, M.A. Miller, M.C. Rota, et al., Trends for Influenza-related Deaths during Pandemic and Epidemic Seasons, Italy, 1969–2001, Emerg. Infect. Dis., 13 (2007), 694–699. https://doi.org/10.3201/eid1305.061309 doi: 10.3201/eid1305.061309

  • This article has been cited by:

    1. Guihong Fan, Junli Liu, P. van den Driessche, Jianhong Wu, Huaiping Zhu, The impact of maturation delay of mosquitoes on the transmission of West Nile virus, 2010, 228, 00255564, 119, 10.1016/j.mbs.2010.08.010
    2. Pierre Magal, Ousmane Seydi, Glenn Webb, Final Size of an Epidemic for a Two-Group SIR Model, 2016, 76, 0036-1399, 2042, 10.1137/16M1065392
    3. Pierre Magal, Ousmane Seydi, Glenn Webb, Final size of a multi-group SIR epidemic model: Irreducible and non-irreducible modes of transmission, 2018, 301, 00255564, 59, 10.1016/j.mbs.2018.03.020
    4. Subekshya Bidari, Xinying Chen, Daniel Peters, Dylanger Pittman, Péter L. Simon, Solvability of implicit final size equations for SIR epidemic models, 2016, 282, 00255564, 181, 10.1016/j.mbs.2016.10.012
    5. Zhiying Wang, Jing Liang, Huifang Nie, Hongli Zhao, A 3SI3R model for the propagation of two rumors with mutual promotion, 2020, 2020, 1687-1847, 10.1186/s13662-020-02552-w
    6. Emmanuelle Augeraud-Véron, E. Augeraud, M. Banerjee, J.-S. Dhersin, A. d'Onofrio, T. Lipniacki, S. Petrovskii, Chi Tran, A. Veber-Delattre, E. Vergu, V. Volpert, Lifting the COVID-19 lockdown: different scenarios for France, 2020, 15, 0973-5348, 40, 10.1051/mmnp/2020031
    7. KLOT PATANARAPEELERT, INVESTIGATING THE ROLE OF WITHIN- AND BETWEEN-PATCH MOVEMENT IN A DYNAMIC MODEL OF DISEASE SPREAD, 2020, 28, 0218-3390, 815, 10.1142/S0218339020500187
    8. Aadrita Nandi, Linda J. S. Allen, 2019, Chapter 20, 978-3-030-25497-1, 483, 10.1007/978-3-030-25498-8_20
    9. Jingan Cui, Yanan Zhang, Zhilan Feng, Influence of non-homogeneous mixing on final epidemic size in a meta-population model, 2019, 13, 1751-3758, 31, 10.1080/17513758.2018.1484186
    10. Pierre Magal, Glenn Webb, The parameter identification problem for SIR epidemic models: identifying unreported cases, 2018, 77, 0303-6812, 1629, 10.1007/s00285-017-1203-9
    11. Abba B. Gumel, Enahoro A. Iboi, Calistus N. Ngonghala, Elamin H. Elbasha, A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations, 2021, 6, 24680427, 148, 10.1016/j.idm.2020.11.005
    12. Joel C. Miller, A Note on the Derivation of Epidemic Final Sizes, 2012, 74, 0092-8240, 2125, 10.1007/s11538-012-9749-6
    13. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng, 2019, Chapter 5, 978-1-4939-9826-5, 179, 10.1007/978-1-4939-9828-9_5
    14. Fred Brauer, General compartmental epidemic models, 2010, 31, 0252-9599, 289, 10.1007/s11401-009-0454-1
    15. Lei Xiang, Yuyue Zhang, Jicai Huang, Stability analysis of a discrete SIRS epidemic model with vaccination, 2020, 26, 1023-6198, 309, 10.1080/10236198.2020.1725497
    16. Hémaho B. Taboe, Kolawolé V. Salako, James M. Tison, Calistus N. Ngonghala, Romain Glèlè Kakaï, Predicting COVID-19 spread in the face of control measures in West Africa, 2020, 328, 00255564, 108431, 10.1016/j.mbs.2020.108431
    17. Julien Arino, Christopher S Bowman, Seyed M Moghadas, Antiviral resistance during pandemic influenza: implications for stockpiling and drug use, 2009, 9, 1471-2334, 10.1186/1471-2334-9-8
    18. Zhipeng Qiu, Zhilan Feng, Transmission Dynamics of an Influenza Model with Vaccination and Antiviral Treatment, 2010, 72, 0092-8240, 1, 10.1007/s11538-009-9435-5
    19. Kyeongah Nah, Mahnaz Alavinejad, Ashrafur Rahman, Jane M Heffernan, Jianhong Wu, Impact of influenza vaccine-modified infectivity on attack rate, case fatality ratio and mortality, 2020, 492, 00225193, 110190, 10.1016/j.jtbi.2020.110190
    20. Julien Arino, Fred Brauer, P. van den Driessche, James Watmough, Jianhong Wu, A model for influenza with vaccination and antiviral treatment, 2008, 253, 00225193, 118, 10.1016/j.jtbi.2008.02.026
    21. Viggo Andreasen, The Final Size of an Epidemic and Its Relation to the Basic Reproduction Number, 2011, 73, 0092-8240, 2305, 10.1007/s11538-010-9623-3
    22. Calistus N. Ngonghala, Enahoro A. Iboi, Abba B. Gumel, Could masks curtail the post-lockdown resurgence of COVID-19 in the US?, 2020, 329, 00255564, 108452, 10.1016/j.mbs.2020.108452
    23. Keisuke Ejima, Kazuyuki Aihara, Hiroshi Nishiura, Edward Goldstein, The Impact of Model Building on the Transmission Dynamics under Vaccination: Observable (Symptom-Based) versus Unobservable (Contagiousness-Dependent) Approaches, 2013, 8, 1932-6203, e62062, 10.1371/journal.pone.0062062
    24. Hyojung Lee, Sunmi Lee, Chang Hyeong Lee, Stochastic methods for epidemic models: An application to the 2009 H1N1 influenza outbreak in Korea, 2016, 286, 00963003, 232, 10.1016/j.amc.2016.04.019
    25. Bahman Davoudi, Joel C. Miller, Rafael Meza, Lauren Ancel Meyers, David J. D. Earn, Babak Pourbohloul, Early Real-Time Estimation of the Basic Reproduction Number of Emerging Infectious Diseases, 2012, 2, 2160-3308, 10.1103/PhysRevX.2.031005
    26. Tahar Z. Boulmezaoud, E. Augeraud, M. Banerjee, J.-S. Dhersin, A. d'Onofrio, T. Lipniacki, S. Petrovskii, Chi Tran, A. Veber-Delattre, E. Vergu, V. Volpert, A discrete epidemic model and a zigzag strategy for curbing the Covid-19 outbreak and for lifting the lockdown, 2020, 15, 0973-5348, 75, 10.1051/mmnp/2020043
    27. Shi Zhao, Salihu S. Musa, Hao Fu, Daihai He, Jing Qin, Simple framework for real-time forecast in a data-limited situation: the Zika virus (ZIKV) outbreaks in Brazil from 2015 to 2016 as an example, 2019, 12, 1756-3305, 10.1186/s13071-019-3602-9
    28. Yi Wang, Zhouchao Wei, Jinde Cao, Epidemic dynamics of influenza-like diseases spreading in complex networks, 2020, 101, 0924-090X, 1801, 10.1007/s11071-020-05867-1
    29. Carlos Castillo-Chavez, Sunmi Lee, 2015, Chapter 85, 978-3-540-70528-4, 427, 10.1007/978-3-540-70529-1_85
    30. Salisu M. Garba, Jean M.-S. Lubuma, Berge Tsanou, Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa, 2020, 328, 00255564, 108441, 10.1016/j.mbs.2020.108441
    31. Florian Uekermann, Lone Simonsen, Kim Sneppen, Rashid Ansumana, Exploring the contribution of exposure heterogeneity to the cessation of the 2014 Ebola epidemic, 2019, 14, 1932-6203, e0210638, 10.1371/journal.pone.0210638
    32. Calistus N. Ngonghala, Enahoro Iboi, Steffen Eikenberry, Matthew Scotch, Chandini Raina MacIntyre, Matthew H. Bonds, Abba B. Gumel, Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus, 2020, 325, 00255564, 108364, 10.1016/j.mbs.2020.108364
    33. Yi Wang, Jinde Cao, Gang Huang, Further dynamic analysis for a network sexually transmitted disease model with birth and death, 2019, 363, 00963003, 124635, 10.1016/j.amc.2019.124635
    34. Julien Arino, Stéphanie Portet, A simple model for COVID-19, 2020, 5, 24680427, 309, 10.1016/j.idm.2020.04.002
    35. Antoine Danchin, Tuen Wai Ng, Gabriel Turinici, A New Transmission Route for the Propagation of the SARS-CoV-2 Coronavirus, 2020, 10, 2079-7737, 10, 10.3390/biology10010010
    36. Fred Brauer, Epidemic Models with Heterogeneous Mixing and Treatment, 2008, 70, 0092-8240, 1869, 10.1007/s11538-008-9326-1
    37. Nicolas Bacaër, M. Gabriela M. Gomes, On the Final Size of Epidemics with Seasonality, 2009, 71, 0092-8240, 10.1007/s11538-009-9433-7
    38. Juping Zhang, Dan Li, Wenjun Jing, Zhen Jin, Huaiping Zhu, Transmission dynamics of a two-strain pairwise model with infection age, 2019, 71, 0307904X, 656, 10.1016/j.apm.2019.03.001
    39. Jiajia Wang, Laijun Zhao, Rongbing Huang, 2SI2R rumor spreading model in homogeneous networks, 2014, 413, 03784371, 153, 10.1016/j.physa.2014.06.053
    40. Zhilan Feng, John W. Glasser, 2021, 9780128160787, 331, 10.1016/B978-0-12-801238-3.11471-0
    41. Fengqin Zhang, Jianquan Li, Jia Li, Epidemic characteristics of two classic SIS models with disease-induced death, 2017, 424, 00225193, 73, 10.1016/j.jtbi.2017.04.029
    42. Yaming Zhang, Yanyuan Su, Li Weigang, Haiou Liu, Rumor and authoritative information propagation model considering super spreading in complex social networks, 2018, 506, 03784371, 395, 10.1016/j.physa.2018.04.082
    43. Jonathan Dushoff, Sang Woo Park, Speed and strength of an epidemic intervention, 2021, 288, 0962-8452, 10.1098/rspb.2020.1556
    44. Gerardo Chowell, Fred Brauer, 2009, Chapter 1, 978-90-481-2312-4, 1, 10.1007/978-90-481-2313-1_1
    45. Karly A. Jacobsen, Mark G. Burch, Joseph H. Tien, Grzegorz A. Rempała, The large graph limit of a stochastic epidemic model on a dynamic multilayer network, 2018, 12, 1751-3758, 746, 10.1080/17513758.2018.1515993
    46. Yaming Zhang, Yanyuan Su, Li Weigang, Haiou Liu, Interacting model of rumor propagation and behavior spreading in multiplex networks, 2019, 121, 09600779, 168, 10.1016/j.chaos.2019.01.035
    47. Seoyun Choe, Sunmi Lee, Modeling optimal treatment strategies in a heterogeneous mixing model, 2015, 12, 1742-4682, 10.1186/s12976-015-0026-x
    48. A Ducrot, P Magal, T Nguyen, G F Webb, Identifying the number of unreported cases in SIR epidemic models, 2020, 37, 1477-8599, 243, 10.1093/imammb/dqz013
    49. Fan Bai, Uniqueness of Nash equilibrium in vaccination games, 2016, 10, 1751-3758, 395, 10.1080/17513758.2016.1213319
    50. Julien Arino, Mathematical epidemiology in a data-rich world, 2020, 5, 24680427, 161, 10.1016/j.idm.2019.12.008
    51. Fred Brauer, James Watmough, Age of infection epidemic models with heterogeneous mixing, 2009, 3, 1751-3758, 324, 10.1080/17513750802415822
    52. Salihu Sabiu Musa, Shi Zhao, Nafiu Hussaini, Salisu Usaini, Daihai He, Dynamics analysis of typhoid fever with public health education programs and final epidemic size relation, 2021, 10, 25900374, 100153, 10.1016/j.rinam.2021.100153
    53. Franco Blanchini, Paolo Bolzern, Patrizio Colaneri, Giuseppe De Nicolao, Giulia Giordano, Optimal control of compartmental models: The exact solution, 2023, 147, 00051098, 110680, 10.1016/j.automatica.2022.110680
    54. Salihu S. Musa, Abdullahi Yusuf, Shi Zhao, Zainab U. Abdullahi, Hammoda Abu-Odah, Farouk Tijjani Saad, Lukman Adamu, Daihai He, Transmission dynamics of COVID-19 pandemic with combined effects of relapse, reinfection and environmental contribution: A modeling analysis, 2022, 38, 22113797, 105653, 10.1016/j.rinp.2022.105653
    55. Franco Blanchini, Paolo Bolzern, Patrizio Colaneri, Giuseppe De Nicolao, Giulia Giordano, 2022, Logarithmic Dynamics and Aggregation in Epidemics, 978-1-6654-6761-2, 4313, 10.1109/CDC51059.2022.9992421
    56. Alison Adams, Quiyana M. Murphy, Owen P. Dougherty, Aubrey M. Sawyer, Fan Bai, Christina J. Edholm, Evan P. Williams, Linda J.S. Allen, Colleen B. Jonsson, Data-driven models for replication kinetics of Orthohantavirus infections, 2022, 349, 00255564, 108834, 10.1016/j.mbs.2022.108834
    57. Asma Azizi, Caner Kazanci, Natalia L. Komarova, Dominik Wodarz, Effect of Human Behavior on the Evolution of Viral Strains During an Epidemic, 2022, 84, 0092-8240, 10.1007/s11538-022-01102-7
    58. Yi Wang, Jinde Cao, Changfeng Xue, Li Li, Mathematical Analysis of Epidemic Models with Treatment in Heterogeneous Networks, 2023, 85, 0092-8240, 10.1007/s11538-022-01116-1
    59. Florin Avram, Rim Adenane, David I. Ketcheson, A Review of Matrix SIR Arino Epidemic Models, 2021, 9, 2227-7390, 1513, 10.3390/math9131513
    60. Xiaohao Guo, Yichao Guo, Zeyu Zhao, Shiting Yang, Yanhua Su, Benhua Zhao, Tianmu Chen, Computing R0 of dynamic models by a definition-based method, 2022, 7, 24680427, 196, 10.1016/j.idm.2022.05.004
    61. 2022, chapter 3, 9781799883432, 56, 10.4018/978-1-7998-8343-2.ch003
    62. Cameron J. Browne, Hayriye Gulbudak, Joshua C. Macdonald, Differential impacts of contact tracing and lockdowns on outbreak size in COVID-19 model applied to China, 2022, 532, 00225193, 110919, 10.1016/j.jtbi.2021.110919
    63. Yan Chen, Haitao Song, Shengqiang Liu, Evaluations of COVID-19 epidemic models with multiple susceptible compartments using exponential and non-exponential distribution for disease stages, 2022, 7, 24680427, 795, 10.1016/j.idm.2022.11.004
    64. Luis Almeida, Pierre-Alexandre Bliman, Grégoire Nadin, Benoît Perthame, Nicolas Vauchelet, Final size and convergence rate for an epidemic in heterogeneous populations, 2021, 31, 0218-2025, 1021, 10.1142/S0218202521500251
    65. Jaafar El Karkri, Mohammed Benmir, 2022, 9780323905046, 137, 10.1016/B978-0-32-390504-6.00014-0
    66. Natali Hritonenko, Olga Yatsenko, Yuri Yatsenko, Model with transmission delays for COVID‐19 control: Theory and empirical assessment, 2022, 24, 1097-3923, 1218, 10.1111/jpet.12554
    67. Jummy F. David, Sarafa A. Iyaniwura, Michael J. Ward, Fred Brauer, A novel approach to modelling the spatial spread of airborne diseases: an epidemic model with indirect transmission, 2020, 17, 1551-0018, 3294, 10.3934/mbe.2020188
    68. Qiang Huang, Qiyong Liu, Ci Song, Xiaobo Liu, Hua Shu, Xi Wang, Yaxi Liu, Xiao Chen, Jie Chen, Tao Pei, Urban spatial epidemic simulation model: A case study of the second COVID‐19 outbreak in Beijing, China, 2022, 26, 1361-1682, 297, 10.1111/tgis.12850
    69. Ashabul Hoque, Abdul Malek, K. M. Rukhsad Asif Zaman, Data analysis and prediction of the COVID-19 outbreak in the first and second waves for top 5 affected countries in the world, 2022, 109, 0924-090X, 77, 10.1007/s11071-022-07473-9
    70. Jiaqi Liu, Jiayin Qi, Online Public Rumor Engagement Model and Intervention Strategy in Major Public Health Emergencies: From the Perspective of Social Psychological Stress, 2022, 19, 1660-4601, 1988, 10.3390/ijerph19041988
    71. Florin Avram, Rim Adenane, Andrei Halanay, New Results and Open Questions for SIR-PH Epidemic Models with Linear Birth Rate, Loss of Immunity, Vaccination, and Disease and Vaccination Fatalities, 2022, 14, 2073-8994, 995, 10.3390/sym14050995
    72. Jummy F. David, Sarafa A. Iyaniwura, Effect of Human Mobility on the Spatial Spread of Airborne Diseases: An Epidemic Model with Indirect Transmission, 2022, 84, 0092-8240, 10.1007/s11538-022-01020-8
    73. Julien Arino, Pierre-Yves Boëlle, Evan Milliken, Stéphanie Portet, Risk of COVID-19 variant importation – How useful are travel control measures?, 2021, 6, 24680427, 875, 10.1016/j.idm.2021.06.006
    74. Sedrique A. Tiomela, J.E. Macías-Díaz, Alain Mvogo, Computer simulation of the dynamics of a spatial susceptible-infected-recovered epidemic model with time delays in transmission and treatment, 2021, 212, 01692607, 106469, 10.1016/j.cmpb.2021.106469
    75. Florin Avram, Rim Adenane, Lasko Basnarkov, Gianluca Bianchin, Dan Goreac, Andrei Halanay, An Age of Infection Kernel, an R Formula, and Further Results for Arino–Brauer A, B Matrix Epidemic Models with Varying Populations, Waning Immunity, and Disease and Vaccination Fatalities, 2023, 11, 2227-7390, 1307, 10.3390/math11061307
    76. Bolarinwa Bolaji, B. I. Omede, U. B. Odionyenma, P. B. Ojih, Abdullahi A. Ibrahim, Modelling the transmission dynamics of Omicron variant of COVID-19 in densely populated city of Lagos in Nigeria, 2023, 2714-4704, 1055, 10.46481/jnsps.2023.1055
    77. Wanxiao Xu, Hongying Shu, Lin Wang, Xiang-Sheng Wang, James Watmough, The importance of quarantine: modelling the COVID-19 testing process, 2023, 86, 0303-6812, 10.1007/s00285-023-01916-6
    78. Sarita Bugalia, Jai Prakash Tripathi, Assessing potential insights of an imperfect testing strategy: Parameter estimation and practical identifiability using early COVID-19 data in India, 2023, 10075704, 107280, 10.1016/j.cnsns.2023.107280
    79. Carles Barril, Pierre-Alexandre Bliman, Sílvia Cuadrado, Final Size for Epidemic Models with Asymptomatic Transmission, 2023, 85, 0092-8240, 10.1007/s11538-023-01159-y
    80. Jean-Jil Duchamps, Félix Foutel-Rodier, Emmanuel Schertzer, General epidemiological models: law of large numbers and contact tracing, 2023, 28, 1083-6489, 10.1214/23-EJP992
    81. Maximilian M. Nguyen, Ari S. Freedman, Sinan A. Ozbay, Simon A. Levin, Fundamental bound on epidemic overshoot in the SIR model, 2023, 20, 1742-5662, 10.1098/rsif.2023.0322
    82. Mohamed Anass El Yamani, Jaafar El Karkri, Saiida Lazaar, Rajae Aboulaich, A two-group epidemiological model: Stability analysis and numerical simulation using neural networks, 2023, 14, 1793-9623, 10.1142/S1793962323500290
    83. Preeti Deolia, Anuraj Singh, Analysing the probable insights of ADE in dengue vaccination embodying sequential Zika infection and waning immunity, 2024, 139, 2190-5444, 10.1140/epjp/s13360-023-04813-5
    84. Donald S. Burke, Origins of the problematic E in SEIR epidemic models, 2024, 24680427, 10.1016/j.idm.2024.03.003
    85. Alexis Erich S. Almocera, Alejandro H. González, Esteban A. Hernandez-Vargas, Confinement tonicity on epidemic spreading, 2024, 88, 0303-6812, 10.1007/s00285-024-02064-1
    86. Qian Li, Biao Tang, Yanni Xiao, Multiple epidemic waves in a switching system with multi-thresholds triggered alternate control, 2024, 112, 0924-090X, 8721, 10.1007/s11071-024-09533-8
    87. A. Dénes, G. Röst, T. Tekeli, 2024, Chapter 12, 978-3-031-59071-9, 249, 10.1007/978-3-031-59072-6_12
    88. Francesca Calà Campana, Rami Katz, Giulia Giordano, Sequential-Quadratic-Hamiltonian Optimal Control of Epidemic Models With an Arbitrary Number of Infected and Non-Infected Compartments, 2024, 8, 2475-1456, 1805, 10.1109/LCSYS.2024.3412775
    89. Komal Tanwar, Nitesh Kumawat, Jai Prakash Tripathi, Sudipa Chauhan, Anuj Mubayi, Evaluating vaccination timing, hesitancy and effectiveness to prevent future outbreaks: insights from COVID-19 modelling and transmission dynamics, 2024, 11, 2054-5703, 10.1098/rsos.240833
    90. Justin K. Sheen, Lee Kennedy-Shaffer, Michael Z. Levy, Charlotte Jessica E. Metcalf, Claudio José Struchiner, Design of field trials for the evaluation of transmissible vaccines in animal populations, 2025, 21, 1553-7358, e1012779, 10.1371/journal.pcbi.1012779
    91. Rim Adenane, Mohamed El Fatini, 2024, Actuarial Risks Associated to Disease Outbreaks and Insurance Plans Under Media Coverage Strategy, 979-8-3503-8735-3, 1, 10.1109/ICOA62581.2024.10754019
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(1549) PDF downloads(71) Cited by(3)

Preview PDF
Download XML
Export Citation
Article outline
Abstract
References

Figures and Tables

Figures(1)  /  Tables(2)

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog