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Exponential Growth Trajectory – The Math Behind Corona Spread

Let me ask you a question – how is the social distancing going? Our lives were going smooth, we were partying, enjoying our lives, bitching about the governments, and going to work (even if we hate it), and living our lives normally. Suddenly there was a murmur about a new deadly virus affecting Chinese citizens living in China. We didn’t spare any thought as the virus was not impacting us – it was not our problem. Few days and it started impacting us as the reported cases skyrocketed. We were concerned, a little anxious, but it was just a news of faraway land and BOOM, the stats hit us with a force which is unmatchable to anything we have seen before. 

Suddenly your neighbor tested positive and Covid is now your problem. It is few step away from you and the governments shut down entire countries to prevent the spread of infection. As it is now our problem, we are hoarding toilet papers and food to survive the pandemic. We are ordering hundreds of masks off amazon to protect ourselves and our families.

How did we come to this when it is expected that the virus initially infected a single person. We can call this infectious person patient 1. Patient one was the host to the virus, he was mingling, drinking, clubbing, and socializing without knowing that he is infecting other. The dilemma of the spread of Corona virus is severe and the answer to the questions are related to mathematics. Exponential growth trajectory is your answer to all the questions related to the spread of Corona Virus.  

Exponential growth is one of the most powerful tool of nature. Let me prove this statement with an example. In 1859, there was an English Farmer Thomas Austin. He migrated to Australia and brought 24 rabbits with him. The rabbits liked the environment and started to reproduce. By 1865, in less than 6 years, the number of rabbit population raised to 2 billion. The exponential growth is one of the most effective tool to reproduce and Corona is no exception.

Patient 1 was responsible for spreading the virus to 2.5 individuals, each of them infected 2.5 person and the virus transmission rate exploded. Each infected person is expected to infect a certain number of people which is estimated to be around 2.5 right now, who each in turn go on to infect 2.5 more, and on and on, unless drastic measures are taken to reduce social contact and isolate the infected from others. To evaluate the scope of the infection, think about counting doubles – 1, 2, 4, 8, 16, 32, 64 and so on. How many times would you have to double to get to more than 1 million? 20. How many doubles to get to more than 16 million? 24. Human population also follow the exponential growth pattern hence we are short of natural resources as the population of the world is growing exponentially. Since past few decades, we are listening to the debates discussion alarming rate of population growth and now the debate switched to covid spread.

Why are the governments focused on social distancing, let me tell you all about this dilemma. There was patient of covid, patient 31, he is responsible of infecting almost 1,160 healthy individuals and introduced a new cluster of infection. As he was initially asymptomatic and he was social (maybe too social), he lived his normal life and introduced a whole cluster of infection, an achievement which is not remarkable at all. Moral of the when hospitals are overcrowded, medical supplies are limited, population is stressed, and hospital staff story – don’t be like patient 31!

In this dire situation is overworked – prevention of infection through social distancing is our only hope. As we don’t have the treatment options, prevention is our only weapon. When new hosts are not exposed to the virus, the curve of infection will drop indicating that the condition is under control. 

There is a hope that the infection cannot always grow exponentially, as people become resistant and new intervention are introduced, the rate of the infection is bound to drop. Till then we have to utilize the only option we have – prevention via distancing ourselves. Right now what we all need is play our part and stick to the quarantine regime so we can buy valuable time for healthcare providers to deal with the situation and come up with an effective treatment plan. 

Currently the number of Corona cases are doubling after every 6 days and this is a clear indication of how fast the virus is infecting. Till we come up with the strategy to treat the symptoms, it’s all about limit your social activity and stay at home – not only for your own sake, but for the sake of your loved ones too!