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  • Kalyan K Mohanty

COVID-19 Forecasting with SIR model

Coronavirus disease 2019 (COVID-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The disease was first identified in December 2019 in Wuhan, the capital of China's Hubei province, and has since spread globally, resulting in the ongoing 2019–20 coronavirus pandemic. Common symptoms include fever, cough, and shortness of breath. Other symptoms may include fatigue, muscle pain, diarrhea, sore throat, loss of smell, and abdominal pain. While the majority of cases result in mild symptoms, some progress to viral pneumonia and multi-organ failure. As of 30 April 2020, more than 3.2 million cases have been reported in more than 200 countries and territories, resulting in more than 2,28,057 deaths. More than 9,85,957 people have recovered.

The objective of this work is to analyze susceptible, Infectious, and recovered using the SIR model.


Total Population

The highly populated country has more chances to get infected quickly. The following are top populated countries across the globe.



The number of the day goes out

There are different age groups people who go outside on different days. So here we have analyzed which age group has most days outside the home. The more they go outside can have more chances to infected by the COVID-19 virus.


The people of age group 26 – 65 go outside approximately 5 or 6 days a week. So they can get in contact with other infected people as compared to another age group.


Grouping by growth factor

The number of confirmed cases is increasing in many countries, but there are two countries. In a first-type country, the growth factor is larger than 1 and the number of cases is rapidly increasing. In a second-type country, the growth factor is less than 1. Calculate the growth factor

Growth Factor = (ΔC_n )/(ΔC_(n-1) )

Where C is the number of confirmed cases Out breaking: growth factor >> 1 for the last 7 days Stopping: growth factor << 1 for the last 7 days At a crossroad: the others


Group 1: Out breaking, growth factor >> 1 for the last 7 days


Group 2: Stopping, growth factor << 1 for the last 7 days


Group 3: The others


SIR Model


A SIR model is an epidemiological model that computes the theoretical number of people infected with a contagious illness in a closed population over time. The name of this class of models derives from the fact that they involve coupled equations relating the number of susceptible people S (t), number of people infected I (t), and number of people who have recovered R (t). One of the simplest SIR models is the Kermack - McKendrick model.


Non-dimensional SIR model

To simplify the model, we will remove the units of the variables from ODE (Ordinary Differential Equation).

Set (S, I, R) = N × (x, y, z) and (T, β, γ) = (τt, τ -1ρ, τ −1σ) dx/dt = -ρxy (1) dy/dt = -ρxy- σy (2) dz/dt = σy (3)

Where N is the total population and τ is a coefficient ([min], is an integer to simplify). The range of variables and parameters:

0 ≤ (x, y, z, ρ, σ ) ≤ 1 1 ≤ τ ≤ 1440

Basic reproduction number, Non-dimensional parameter, is defined as

R0 = ρσ−1 = βγ−1

Estimated Mean Values of R0: R0 means "the average number of secondary infections caused by an infected host" When

X=1/R_0 =dy/dt =0 (4)

(Global prediction using the SIR model. X: Susceptible, Y: Infected, Z: Recovered)

India

India seems to get its peak around the first week of May after that the number of cases will slow down.


China

China got its peak after 39 days of the first case then after around 30 days the curve flattened.


Remark:

China got its peak after 30 days. Compared to china India will get its peak after 50 days of its first case which shows a better result.


LInk to github: https://github.com/KalyanMohanty/COVID-19_Forecasting_with_SIR_model

Link to Kaggle: https://www.kaggle.com/kalyanmohanty/forecasting-with-sir-model

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