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A Two-Step Polynomial and Nonlinear Growth Approach for Modeling COVID-19 Cases in Mexico

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  • Rafael Pérez Abreu C.

    (Aguascalientes Campus, Centro de Investigación en Matemáticas, A. C., Calzada de la Plenitud 103, José Vasconcelos Calderón, Aguascalientes 20200, Mexico)

  • Samantha Estrada

    (Department of Psychology and Counseling, University of Texas at Tyler, 3900 University Blvd, Tyler, TX 75799, USA)

  • Héctor de-la-Torre-Gutiérrez

    (Aguascalientes Campus, Centro de Investigación en Matemáticas, A. C., Calzada de la Plenitud 103, José Vasconcelos Calderón, Aguascalientes 20200, Mexico)

Abstract

Since December 2019, the novel coronavirus (SARS-CoV-2) and its associated illness COVID-19 have rapidly spread worldwide. The Mexican government has implemented public safety measures to minimize the spread of the virus. In this paper, we used statistical models in two stages to estimate the total number of coronavirus (COVID-19) cases per day at the state and national levels in Mexico. In this paper, we propose two types of models. First, a polynomial model of the growth for the first part of the outbreak until the inflection point of the pandemic curve and then a second nonlinear growth model used to estimate the middle and the end of the outbreak. Model selection was performed using Vuong’s test. The proposed models showed overall fit similar to predictive models (e.g., time series and machine learning); however, the interpretation of parameters is simpler for decisionmakers, and the residuals follow the expected distribution when fitting the models without autocorrelation being an issue.

Suggested Citation

  • Rafael Pérez Abreu C. & Samantha Estrada & Héctor de-la-Torre-Gutiérrez, 2021. "A Two-Step Polynomial and Nonlinear Growth Approach for Modeling COVID-19 Cases in Mexico," Mathematics, MDPI, vol. 9(18), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2180-:d:630519
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    References listed on IDEAS

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    1. Chakraborty, Tanujit & Ghosh, Indrajit, 2020. "Real-time forecasts and risk assessment of novel coronavirus (COVID-19) cases: A data-driven analysis," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
    3. Zhang, Xiaolei & Ma, Renjun & Wang, Lin, 2020. "Predicting turning point, duration and attack rate of COVID-19 outbreaks in major Western countries," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    4. Chimmula, Vinay Kumar Reddy & Zhang, Lei, 2020. "Time series forecasting of COVID-19 transmission in Canada using LSTM networks," Chaos, Solitons & Fractals, Elsevier, vol. 135(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. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
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