Major Project
Presentation
Modelling Logistic Growth Model For COVID-19
Pandemic in India
Under The Supervision Of
Ms Minni Jain
Submitted By:
Prajwal Kumar Bhati (2K16/CO/225)
Pranav Kataria (2K16/CO/229)
Rohit Kumar (2K16/CO/258)
Modelling Logistic Growth Models For
COVID-19 Pandemic In India
Accepted in IEEE 5th
International Conference on
Communication and
Electronics Systems
(ICCES 2020)
Scopus Source: 21100810605
• The effect of COVID-19 has been successfully
controlled in India, by using the technique of National
Lockdown, but it has spread in many countries at a
very rapid rate. Here, we are using phenomenological
models to find the development of Covid-19 pandemic
in India and the impact of lockdown on the number of
infected people in India.
INTRODUCTION
• To officially announce the number of infected cases in
India, we have used growth models. Each growth
model has a different lower and upper bound for our
result. We tried to document the stages of the covid19 pandemic in India. The extreme taken by India is
very effective with some variation across all parts of
India. Here, using this paper we want to understand
about the rate at which this outbreak has occurred in
India. Using generalized growth modelling, we have
mapped out the growth rate of the pandemic in India.
Why Logistic Growth ?
• The reason to use Logistic
Growth for modeling the
Coronavirus outbreak is that
epidemiologists have studied
those types of outbreaks and
it is well known that the first
period of an epidemic follows
Exponential Growth and that
the total period can be
modeled with a Logistic
Growth.
DATASET
SOURCES
• The dataset is sourced from the COVID-19
Patient Database which consists of total
confirmed cases state wise consisting of
patient number, patient gender, age-bracket,
travel history, detected city and current
status for all cities in India. The data is
updated daily. In this report we have used
the data from Jan 31 when the first case in
India was reported to Apr 10 and used the
models to forecast outbreak for next 5 to 10
days.
Major Epidemic
Growth Models
Nonlinear Least Squares for India’s Logistic Growth
When looking at the data, we only have the number of cases per day. We also have the
formula that we want to apply, but we do not yet have the correct values of the
parameters r, K and p in the formula(s).
Unfortunately, it is not possible to rewrite the Logistic Function as a Linear Regression, as
is possible for the Exponential model. We will therefore need a more complex method:
Nonlinear Least Squares estimation using Levenberg Marquardt Algorithm
Steps of Model
Parameter Estimation
• Logistic Model (Lower Bound) {Best Case} [C,r,K]
• Generalized Logistic Model (Average Case) [p,r,K]
• Generalized Growth Model (Upper Bound) {Worst Case} [p,r]
Results
• Total No of cases
• Daily increase in number of cases
• Daily growth rate of cases
RESULTS
Total Number Of Confirmed Cases vs No. Of Days
RESULTS
Daily Increase
Of Confirmed Cases vs
No. Of Days
RESULTS
Daily Growth
Rate Of Confirmed Cases
vs No. Of Days
Short Term
Forecast
Day
Date
Actual
Predicted
Accuracy
(%)
72
11 April 2020
854
677
79.27
73
12 April 2020
758
730
96.30
74
13 April 2020
1243
787
63.31
75
14 April 2020
1031
847
82.15
76
15 April 2020
886
911
97.25
77
16 April 2020
1061
978
92.17
78
17 April 2020
922
1188
77.6
79
18 April 2020
1371
1268
92.48
80
19 April 2020
1580
1274
80.63
We predict a high level risk in India with approximate total actual
cases on April 14 to be 12116 (i.e. 95 % CI: [11895, 12336]), 25706
(i.e. 95 % CI: [25337, 26034]) by April 20. The parameter 𝑝 of the
GLM is estimated as 0.99 (95% CI: [0.98, 1]).
Conclusion
and Future
Work
This confirms that the growth is close to exponential, indicating that
local transmission channels in India are not yet under control
despite National Lockdown.
Actual number of cases recorded match the number of cases
predicted by the models designed. This indicates that we can use
these models to estimate the growth in number of cases in the
future, and can take definitive and decisive decisions based on them.
With a thoroughly validated model, this type of information could
be used by policymakers to estimate how to take the right
measures. Future work involves to follow closely whether future
trends follow the selected model(s).
References
• Ke Wu1,2, Didier Darcet3, Qian Wang4 and Didier Sornette. Generalized logistic growth
modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world.
Preprint at: https://www.medrxiv.org/content/10.1101/2020.03.11.20034363v1
• Chowell et al., 2007; Chowell et al., 2006a. Transmission dynamics of the great influenza
pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions.
Preprint at: https://www.sciencedirect.com/science/article/abs/pii/S0022519305005096
• COVID-19 Patient Database for India available at
https://docs.google.com/spreadsheets/d/e/2PACX-1vSz8Qs1gE_IYpzlkFkCXGcL_BqR8hZieWVirphN1gfrO3H4lDtVZs4kd0C3P8Y9lhsT1rhoB-Q_cP4/pubhtml#
• Tian-Mu Chen, Jia Rui, Qiu-Peng Wang,Ze-Yu Zhao, Jing-An Cui, Ling Yin;A mathematical model
for simulating the phase-based transmissibility of a novel
coronavirus. https://doi.org/10.1186/s40249-020-00640-3
Accepted in IEEE 5th International
Conference on Communication
and Electronics Systems
(ICCES 2020)
Scopus Source: 21100810605
Communicated on: 5th May 2020
Accepted On: 12 May 2020
Registration Proof
Scopus Index Proof