433 - Mathematical Modeling of COVID-19 Transmission by a k Phases SEIR Model

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Presenting Author(s)

Braulio Roberto Gonçalves Marinho Couto

Professor (PhD)
Centro Universitário de Belo Horizonte
Belo Horizonte, Minas Gerais, Brazil
Disclosure: I do not have any relevant financial / non-financial relationships with any proprietary interests.

Co-Author(s)

CE

Carlos Ernesto Ferreira Starling

MD
Lifecenter Hospital
Belo Horizonte, Minas Gerais, Brazil
Disclosure: I do not have any relevant financial / non-financial relationships with any proprietary interests.

Background: Mathematical models can provide insights on the spread of infectious diseases, such as the novel SARS-CoV-2 (COVID-19). This work applied a SEIR epidemiological compartmental model (susceptible-exposed-infected-recovered) with k phases to predict the actual spread of the COVID-19 virus.Fig. 1 – SEIR model for COVID-19.

Methods: Four parameters of the SEIR model were obtained by international experiences: the incubation period = 3.7 in days, the proportion of critical cases = 0.05, the overall case-fatality rate = 0.023, and the asymptomatic proportion of COVID-19 = 0.18. The critical step in the prediction of COVID-19 by the model is the value of R0 (the basic reproduction number) and T_infectious (the infectious period, in days). R0 and T_infectious for each phase of the curve are calculated by mathematical constrained optimization, a numerical method. Differently from a statistical modelling, a numerical method is a type of mathematical modelling that is not dependent on a probability distribution. The objective function that measures the model error is minimized with respect to R0 and T_infectious in the presence of constraints on those variables. For R0, constraints are valid range of values (0.5 ≤ R0 ≤ 20). For T_infectious, constraints also are related to its range of values (2 ≤ T_infectious ≤ 14). A Solver from Excel or NEOS Server, for example, can be used for finding numerically minimum of a function Z, that represents the sum of absolute value of errors between COVID-19 new cases observed in one day, and COVID-19 cases predicted by the SEIR model (Fig. 2 and 3).Fig. 2 - Mathematical Modeling of COVID-19 transmission by a SEIR model wiht three phases.

Fig.3 - Algorithm for the SEIR model applied to COVID-19 (calculation of new COVID-19 cases day-by-day).

Results: The ECDC has registered 8,142,129 COVID-19 in the world on Jun/17/2020. R0 and T_infectious calculated for a three phases curve in USA, with a stabilized scenario (Fig. 4: R0_1=1.0; T_infectious_1=2; R0_2=17.4; T_infectious_2=2; R0_3=1.0; T_infectious_3=14), a two phases curve in Brazil (Fig. 5: R0_1=8.0; T_infectious_1=9; R0_2=1.3; T_infectious_2=6), and a three phases model for France (Fig. 6: R0_1=4.3; T_infectious_1=11; R0_2=9.3; T_infectious_2=11; R0_3=0.5; T_infectious_3=12).Fig. 4 - Three phases SEIR models for R0 and T_infectious that minimize the model error in predicting new COVID-19 cases day-by-day in USA.

Fig. 5 - Two phases SEIR models for R0 and T_infectious that minimize the model error in predicting new COVID-19 cases day-by-day in USA.

Fig. 6 - Two phases SEIR models for R0 and T_infectious that minimize the model error in predicting new COVID-19 cases day-by-day in USA.

Conclusion: The k phases SEIR model proved to be a useful to measure the COVID-19 transmission in a City, State or Country. More phases can be applied to fit a scenario with a new second COVID wave.