A mathematical model based on principles of epidemiology has been developed to study the spread of Covid-19. The model is very simple in approach, and considers only three basic parameters — the rate constant of the spread of the virus to uninfected people before any restrictions, the attenuation (damping) multiplication factor for the rate constant when restrictions such as social distancing or a lockdown are imposed, and the death rate (percentage of confirmed cases resulting in death). The model also assumes that the duration of the illness is 14 days.
The model is first validated by matching the data on total positive cases and deaths from the start of the exponential phase of the epidemic to today, and then extrapolated to the future assuming that the latest behavior of the spread of the virus will continue in the future. Understanding of predictions should be tempered with the realization that people's behavior can change in the future, and how they follow restrictions in the future may not be the same as how they do now. Yet, the present is our only clue to understanding the future.
The model is first calibrated for 10 regions (countries or cities): Spain, Italy, France, Germany, the UK, New York City, India, Australia, New Zealand, and South Korea. Once the parameters for the infection are found for each country, the model is extended for a total period of one year from the start of the epidemic. It is seen that the end date of restrictions has a huge impact on the long-term prognosis for each country. It is also seen that countries that impose harsh lockdowns do not necessarily do better than countries that are more liberal in their restrictions. What is important is how well the people actually obey the spirit of the restrictions. This is clearly seen in countries like France and India, which have imposed punitive lockdowns, and yet in which the number of fresh infections has kept rising.
For countries that cannot muster the requisite discipline, a better way to tackle the epidemic would be to protect the old and the immuno-compromised, given that the fatality rate for older people and people with co-morbidities is much higher than the general average.
For details, view the slideshow below.