Has Kerala flattened the COVID-19 Epidemic curve?
An analysis based on SIR Epidemic Model
Over the past few weeks, we have been constantly hearing the term flattening of the curve. Well, what exactly do you mean by flattening of the curve? This is very important in understanding how the spread of an epidemic can be modeled.
“The spread of COVID-19 is not going to follow an exponential curve — and grave errors will follow if analysts believe it will. The number of new cases rises rapidly, peaks, and then declines. It’s called the epidemiological curve. It’s not a theory or hypothesis; it plays out that way every flu season. It is how it has played out in China and Korea for COVID-19. Flattening the peak to avoid overloading the healthcare system is the main medical goal of the seemingly extreme containment policies we have seen to date” — Richard Baldwin, Professor of International Economics at The Graduate Institute, Geneva.
Well, what’s the epidemic curve Professor Richard is talking about?
An epidemic curve, often described as an epidemiological curve, is a statistical graph used in epidemiology to represent the initiation of an outbreak of an epidemic. It can display the severity of the illness, its outliers, its spread over time and its duration of incubation.
The curve refers to the estimated number of individuals who could acquire COVID-19 over a duration of time. The curve takes on various forms, depending on the extent of infection of the virus. This may be a steep curve, whereby the disease spreads exponentially and the total number of cases shoots up to its peak in a few weeks. The faster the rate of infection increases, the quicker the overloading of the local health care system, which goes beyond its ability to treat people.
In comparison, a flatter curve suggests the same number of individuals to be eventually sick, over a longer period. A lower rate of infection means a less overwhelmed medical system, fewer medical visits on any particular day and fewer patients who are kept away from it.
The ideal aim of combating a pandemic or epidemic is to prevent the spread completely. But it’s critical to slow the spread of the epidemic. This decreases the number of cases that are involved at any given time, which in effect allows the government, medical team, and pharmaceutical companies ample time to effectively plan the control strategies.
Technology can also come in handy at these times of desperation, blockchain technology could be one possible way to fight the epidemic, artificial intelligence, machine learning or data science techniques may find applications in analyzing the huge set of data pertaining to COVID19.
Worldwide Cumulative cases as on 14th April 2020
The worldwide COVID19 statistics have already reached whopping numbers and the number of cases are expected to go up drastically in the coming days. To understand the lethality of an epidemic or a pandemic, we need to understand the epidemic or compartmental models, rather than wasting time in exponentially modeling the pandemic.
This article tries to explain the SIR Epidemic model for epidemiology and analyses how the state of Kerala has flattened its epidemic curve. The obvious question in the dubious mind of people would be like “ Why have you selected Kerala Statistics for the same? Well, not because I’m a Keralite, but the mere fact that Kerala has got special appreciation from nations worldwide and the International Media.
Know the SIR Epidemic Model
SIR is one of the simplest and basic methods to model an epidemic. The SIR models the flows of people between three compartments: Susceptible(S), Infected (I), and Removed (R). Each of these variables represents the number of people in those compartments. The beta and gamma parameters largely regulate how frequently people move from Susceptible to Infected to the Removed compartments.
The SIR model is used where individuals infect each other directly. The SIR model is thus perfect to model diseases or epidemics whereby people infect other people and once they get immune, they are no more capable of getting the infection. An individual who recovers from the illness is also modeled to have perfect immunity to the disease thereafter. Contact between people is also modeled to be random. The rate at which people become infected is directly proportional to the number of infected people, and the number of susceptible individuals. If there are lots of people infected, the chances of a susceptible coming into contact with someone who is infected is very high. Likewise, if there are very few susceptible people, the chances of a susceptible coming into contact with an infected are lower (since most of the contact would be between the non-susceptible people — either infected or immune). Solving the ODE’s using any mathematical methods yields the so-called epidemic curve for an epidemic. This was the epidemic curve that we were talking about.
So, now we know which curve the researchers are talking about. Alas, now you know why an epidemic curve should reasonably be different from an exponential curve that people are trying to fit in( Yes, the blue curve you are looking at, the no: of people infected over time). An epidemic cannot go on spreading exponentially affecting the entire population. The peak of the epidemic changes by adjusting the beta and gamma parameters.
Now, see what happens when I try to increase the beta value, keeping gamma constant at the previous rate.
It can be observed that the peak of infection has increased and the peak is now reached at a much faster rate. This is detrimental to society and will undoubtedly be overburden on the local health care system. Self-quarantine and isolation, social distancing can indeed be a great way in which we can delay reaching the peak, by lowering it and by shifting the reach of the peak to a farther time.
SIR Model Infected Curve v/s Kerala Active Cases
I have tried to plot the SIR Infection Curve with currently active cases from the state of Kerala, according to data from government data sources. The basic reproductive number (Ro)of an epidemic is the ratio of beta to the gamma value. An epidemic is considered to grow when Ro is greater than 1 and subsides when R0 is less than 1. The Ro for Covid19 has estimated to be somewhere between 1.5 and 2.5.
The comparison of Actual Data (active cases) with what could have been projection based on the SIR model can be a light at the end of the tunnel. It’s obvious from the graph that Kerala has indeed flattened the curve. But it has to be noted and understood that these estimates fully depend on the parameters and assumptions I have considered for running the SIR Model. My parameter estimations are based on the mean estimated value of Ro (1.96), which could well change over time.
Fighting Corona- Kerala Model
The South Indian state of Kerala, with its much appreciated and effective healthcare system, one of the best in the country, has shown India the way to fight Covid19. The first Covid19 case in India was reported in Kerala on the 30th of January,2020. A medical student who returned to Kerala from Wuhan had been tested positive for Covid19.
Cumulative Cases vs Active Cases in Kerala with LockDown Markers
The graph pretty much is a piece of evidence to presumably assume that the number of active cases in Kerala is going down the timeline. This is indeed a positive sign for the state, which has much been appreciated by the National and International Media for its untiring efforts in curbing the menace of Covid19.
Comparison of Confirmed, Recovered, Dead Cases for various states
As of 14th April 2020, India has around 10,000 confirmed cases, with Maharashtra being the epicenter of Covid19 in India. Kerala with a majority of the NRI population in the country has witnessed an initial surge in the number of cases, mostly imported cases, but with effective measures like home quarantine, airport screening, self-isolation and restrictions imposed by the government, has helped the state climb down the ladder in the total number of cases. As of this date, Kerala has 384 confirmed cases with 174 active cases. Around 211 patients have recovered from the pandemic and the mortality rate in Kerala is one of the least in the country with 0.5 %, compared to the national mortality rate of 3.86%.
What has Kerala done to curb the Pandemic?
The Kerala Government had been instrumental in fighting the pandemic, right from day one. KK Shailaja, the health minister of the state along with the medical team and health officials of the state dealt with Covid19 with iron fists. Having gained courage from the way the state has fought the Nipah virus in 2019, the strategies to be adopted were nothing new to the health department. However, with the lethality of the virus still unknown, without vaccination and seeing the way “The West” has succumbed to the pandemic, Yes, there was initial confusion. Yet, the state has shown immense courage in finding a way out of the epidemic.
I have listed out a few of the notable efforts from Kerala Government in its uncompromising fight against the deadly coronavirus:
COVID Wisk
Kerala became a role model for the entire country as they set up COVID Wisks, the South Korean model walk-in kiosks, where you can get tested. These kiosks can be easily implemented anywhere in the country and Kerala has shown India the way forward to improve the number of testing. The health officials have stated that this is indeed a safe way in which they could collect samples from people who have symptoms of covid19. The kiosks could help health workers to a great extent as they are not exposed.
Publishing Route Maps
The government was instrumental in preparing route maps or flowcharts which listed all the places visited by a susceptible person or a family under quarantine. These flowcharts were prepared with the data collected from the infected person(s) itself and were circulated through social media so that people could willfully inform officials if they had come in contact with them at the mentioned day or time. This initiative was pivotal in identifying new cases and quarantining people.
Community Kitchens
The community kitchens are primarily responsible for the weaker sections of the state, including guest laborers, homeless and the helpless. This move has received National and International acclaim. The workers in the community kitchen maintain social distancing and they are distributing more than two lakh food packets a day. The state has also formed a volunteer group, which includes a lot of youngsters who have readily volunteered their help in distributing the packets.
“Break the Chain” initiative
The health department of Kerala had launched a “break the chain” mission to encourage people to get their hand sanitized to prevent the virus from propagating. This initiative had received widespread popularity. Celebrities were made brand ambassadors for the mission and the people of Kerala wholeheartedly received the initiative.
Summary
In reality, no epidemic model is accurate in forecasting the epidemic trend, as the actual number of cases can shoot up any time which depends on a lot of social and economic parameters which are hard to model mathematically. In this article, I have tried to model the data from Kerala on the SIR Epidemic model, which is the most basic form of the epidemic model. There are a lot of variations to the basic SIR model, but the parameter estimations in such models are not possible at this point, as the epidemic is yet to reach its estimated peak. The crux of the article is, Kerala has indeed been successful in limiting the peak of infection and has undoubtedly, prolonged the peak, at least for now.
And well for my question, “Has Kerala Flattened the COVID19 Epidemic Curve?”, it is left for the reader to understand the facts and decide.
For me, the answer would be an Affirmative YES!
Bibliography
- https://voxeu.org/article/it-s-not-exponential-economist-s-view-epidemiological-curve
- https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology
- https://www.lewuathe.com/covid-19-dynamics-with-sir-model.html
- https://scipython.com/book/chapter-8-scipy/additional-examples/the-sir-epidemic-model/
- http://www.public.asu.edu/~hnesse/classes/sir.html
- https://www.mygov.in/covid-19
- https://medium.com/@aneenaalex/covid-19-pandemic-fight-the-blockchain-way-b83501a3432
