IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v139y2020ics0960077920306937.html
   My bibliography  Save this article

A non-homogeneous Markov early epidemic growth dynamics model. Application to the SARS-CoV-2 pandemic

Author

Listed:
  • Barraza, Néstor Ruben
  • Pena, Gabriel
  • Moreno, Verónica

Abstract

This work introduces a new markovian stochastic model that can be described as a non-homogeneous Pure Birth process. We propose a functional form of birth rate that depends on the number of individuals in the population and on the elapsed time, allowing us to model a contagion effect. Thus, we model the early stages of an epidemic. The number of individuals then becomes the infectious cases and the birth rate becomes the incidence rate. We obtain this way a process that depends on two competitive phenomena, infection and immunization. Variations in those rates allow us to monitor how effective the actions taken by government and health organizations are. From our model, three useful indicators for the epidemic evolution over time are obtained: the immunization rate, the infection/immunization ratio and the mean time between infections (MTBI). The proposed model allows either positive or negative concavities for the mean value curve, provided the infection/immunization ratio is either greater or less than one. We apply this model to the present SARS-CoV-2 pandemic still in its early growth stage in Latin American countries. As it is shown, the model accomplishes a good fit for the real number of both positive cases and deaths. We analyze the evolution of the three indicators for several countries and perform a comparative study between them. Important conclusions are obtained from this analysis.

Suggested Citation

  • Barraza, Néstor Ruben & Pena, Gabriel & Moreno, Verónica, 2020. "A non-homogeneous Markov early epidemic growth dynamics model. Application to the SARS-CoV-2 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920306937
    DOI: 10.1016/j.chaos.2020.110297
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920306937
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110297?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Silva, Petrônio C.L. & Batista, Paulo V.C. & Lima, Hélder S. & Alves, Marcos A. & Guimarães, Frederico G. & Silva, Rodrigo C.P., 2020. "COVID-ABS: An agent-based model of COVID-19 epidemic to simulate health and economic effects of social distancing interventions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Clancy, Damian & O'Neill, Philip, 1998. "Approximation of epidemics by inhomogeneous birth-and-death processes," Stochastic Processes and their Applications, Elsevier, vol. 73(2), pages 233-245, March.
    3. da Silva, Ramon Gomes & Ribeiro, Matheus Henrique Dal Molin & Mariani, Viviana Cocco & Coelho, Leandro dos Santos, 2020. "Forecasting Brazilian and American COVID-19 cases based on artificial intelligence coupled with climatic exogenous variables," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Contreras, Sebastián & Biron-Lattes, Juan Pablo & Villavicencio, H. Andrés & Medina-Ortiz, David & Llanovarced-Kawles, Nyna & Olivera-Nappa, Álvaro, 2020. "Statistically-based methodology for revealing real contagion trends and correcting delay-induced errors in the assessment of COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Ribeiro, Matheus Henrique Dal Molin & da Silva, Ramon Gomes & Mariani, Viviana Cocco & Coelho, Leandro dos Santos, 2020. "Short-term forecasting COVID-19 cumulative confirmed cases: Perspectives for Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    6. Simon, Matthieu, 2020. "SIR epidemics with stochastic infectious periods," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4252-4274.
    7. Ali, Ishtiaq & Ullah Khan, Sami, 2020. "Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    8. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Su, Huishuang & Li, Xue, 2020. "Dynamic behaviors of a two-group stochastic SIRS epidemic model with standard incidence rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Medeiros, Marcelo C. & Street, Alexandre & Valladão, Davi & Vasconcelos, Gabriel & Zilberman, Eduardo, 2022. "Short-term Covid-19 forecast for latecomers," International Journal of Forecasting, Elsevier, vol. 38(2), pages 467-488.
    2. Matheus Henrique Dal Molin Ribeiro & Stéfano Frizzo Stefenon & José Donizetti de Lima & Ademir Nied & Viviana Cocco Mariani & Leandro dos Santos Coelho, 2020. "Electricity Price Forecasting Based on Self-Adaptive Decomposition and Heterogeneous Ensemble Learning," Energies, MDPI, vol. 13(19), pages 1-22, October.
    3. Dalton Garcia Borges de Souza & Erivelton Antonio dos Santos & Francisco Tarcísio Alves Júnior & Mariá Cristina Vasconcelos Nascimento, 2021. "On Comparing Cross-Validated Forecasting Models with a Novel Fuzzy-TOPSIS Metric: A COVID-19 Case Study," Sustainability, MDPI, vol. 13(24), pages 1-25, December.
    4. Đorđević, J. & Papić, I. & Šuvak, N., 2021. "A two diffusion stochastic model for the spread of the new corona virus SARS-CoV-2," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    5. da Silva, Ramon Gomes & Ribeiro, Matheus Henrique Dal Molin & Moreno, Sinvaldo Rodrigues & Mariani, Viviana Cocco & Coelho, Leandro dos Santos, 2021. "A novel decomposition-ensemble learning framework for multi-step ahead wind energy forecasting," Energy, Elsevier, vol. 216(C).
    6. Tayarani N., Mohammad-H., 2021. "Applications of artificial intelligence in battling against covid-19: A literature review," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Hwang, Eunju, 2022. "Prediction intervals of the COVID-19 cases by HAR models with growth rates and vaccination rates in top eight affected countries: Bootstrap improvement," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    8. Fattahi, Mohammad & Keyvanshokooh, Esmaeil & Kannan, Devika & Govindan, Kannan, 2023. "Resource planning strategies for healthcare systems during a pandemic," European Journal of Operational Research, Elsevier, vol. 304(1), pages 192-206.
    9. Andrés Rodríguez‐Pose & Chiara Burlina, 2021. "Institutions and the uneven geography of the first wave of the COVID‐19 pandemic," Journal of Regional Science, Wiley Blackwell, vol. 61(4), pages 728-752, September.
    10. Masum, Mohammad & Masud, M.A. & Adnan, Muhaiminul Islam & Shahriar, Hossain & Kim, Sangil, 2022. "Comparative study of a mathematical epidemic model, statistical modeling, and deep learning for COVID-19 forecasting and management," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    11. Das, Saikat & Bose, Indranil & Sarkar, Uttam Kumar, 2023. "Predicting the outbreak of epidemics using a network-based approach," European Journal of Operational Research, Elsevier, vol. 309(2), pages 819-831.
    12. Moritz Kersting & Andreas Bossert & Leif Sörensen & Benjamin Wacker & Jan Chr. Schlüter, 2021. "Predicting effectiveness of countermeasures during the COVID-19 outbreak in South Africa using agent-based simulation," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-15, December.
    13. Nawin Raj, 2022. "Prediction of Sea Level with Vertical Land Movement Correction Using Deep Learning," Mathematics, MDPI, vol. 10(23), pages 1-23, November.
    14. Crokidakis, Nuno, 2020. "COVID-19 spreading in Rio de Janeiro, Brazil: Do the policies of social isolation really work?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    15. Shen, Meng & Li, Xiang & Lu, Yujie & Cui, Qingbin & Wei, Yi-Ming, 2021. "Personality-based normative feedback intervention for energy conservation," Energy Economics, Elsevier, vol. 104(C).
    16. Ishtiaq Ali & Sami Ullah Khan, 2023. "A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    17. Zachariah Sinkala & Vajira Manathunga & Bichaka Fayissa, 2022. "An Epidemic Compartment Model for Economic Policy Directions for Managing Future Pandemic," Papers 2202.05374, arXiv.org.
    18. Mellacher, Patrick, 2020. "COVID-Town: An Integrated Economic-Epidemiological Agent-Based Model," MPRA Paper 103661, University Library of Munich, Germany.
    19. James, Nick & Menzies, Max, 2023. "Collective infectivity of the pandemic over time and association with vaccine coverage and economic development," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    20. Fernandes, Leonardo H.S. & Silva, José W.L. & de Araujo, Fernando H.A., 2022. "Multifractal risk measures by Macroeconophysics perspective: The case of Brazilian inflation dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920306937. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.