A deductive approach to modeling the spread of COVID-19

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Abstract

Severe acute respiratory syndrome coronavirus 2 (SARS-COV-2), previously known as 2019-nCoV, is responsible for the atypical pneumonia pandemic designated as Coronavirus Disease 2019 (COVID-19). The confirmed number of cases continues to grow exponentially reaching 492,000 people in 175 countries as of March 25, 2020. 22,169 people (~4.5%) infected with SARS-COV-2 virus have died. We have developed an exponential regression model using the COVID-19 case data (Jan 22 – Mar 22, 2020). Our primary model uses designated Phase 1 countries, who exceed 2500 cases on Mar 22. The model is then applied to Phase 2 countries: those that escaped the initial Phase 1 global expansion of COVID-19. With the exception of stabilizing countries (South Korea, Japan, and Iran) all Phase 1 countries are growing exponentially, as per I₂₅₀₀(t)=120.4 × e^0.238t, with a rate, r = 0.238 ± 0.068. Excluding China, the BRICS developing nations and Australia are in Phase 2. Case data from Phase 2 countries are following the model derived from Phase 1 countries. In the absence of measures employed to flatten the curve including social distancing, quarantine, and healthcare expansion, our model projects over 274,000 cases and 12,300 deaths in the US by Mar 31. India can expect 123,000 cases by April 16. By flattening the curve to the growth rate of stabilizing countries (r = 0.044 ± 0.062), the US would prevent 8,500 deaths by Mar 31, and India would prevent 5,500 deaths by April 16.

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Important Equations, Figures, and Tables

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[latexpage] $I_{2500}(t)={120.4\times e}^{0.238t}$

Model Equation 1: Countries Exceeding 2500 cases of COVID-19

[latexpage]
$C_{Phase\ 1}(t)={N_{25-Mar}\times e}^{0.238t}$
$C_{Stabilized}(t)={N_{25-Mar}\times e}^{0.0440t}$
Model Equations 3 and Model Equation 4: $N_{25-Mar}$ as the number of cases in a country on March 25 and t is the number of days after March 25. The growth rates are derived from Tables 1 and 3, respectively.

[latexpage] $PD(t)=CFR\times[C_{Phase\ 1}\left(t\right){-C}_{Stabilized}\left(t\right)]$
Model Equation 5: Preventable deaths with Phase 1 growth. PD is preventable deaths. The case fatality ratio of COVID-19 (CFR) is 4.51%. It is multiplied into the difference of cases between Phase 1 growth and that of stabilizing countries.

Country	N	r	R²
Austria	90.7	0.257	0.99
Belgium	97.6	0.210	0.99
France	103.5	0.236	0.98
Germany	112.3	0.258	0.99
Italy	251.9	0.204	0.97
Netherlands	130.2	0.211	0.99
Norway	132.9	0.191	0.91
Spain	101.4	0.290	0.98
Switzerland	120.7	0.237	0.99
UK	98.7	0.228	0.99
US	84.6	0.295	1.00
Average	120.4	0.238

[latexpage]Table 1: Exponential regression modeling of Phase 1 countries with greater than 2500 cases as of March 22, 2020, for the equation $\ I(t)={N\times e}^{rt}$. R2 correlation coefficients are included per country. An average value for ‘N’ and ‘r’ is calculated. The mean rate of expansion of Phase 1 countries is 0.238, with standard deviation 0.034.

Country	r	R²
Iran	0.075	0.980
Japan	0.046	0.946
South Korea	0.012	0.991
Average	0.044

[latexpage] Table 3: Exponential regression modeling of stabilized countries, from March 12-22, 2020, for the equation $\ I(t)={N\times e}^{rt}$. An average ‘r’ is calculated at 0.044. This post-stabilized average rate of growth is 5.36 and 5.52 times smaller than the average rate of growth of Phase 1 and G7 countries, respectively.

Cite this paper

Mishra P, Mishra S. A deductive approach to modeling the spread of COVID-19. medRxiv. Published online March 26, 2020:2020.03.26.20044651. doi:10.1101/2020.03.26.20044651