The desire to model things dynamical in nature is very strong among mathematicians. Given the current environment, it was natural for us to desire a model which could “explain” various aspects of the spread of COVID-19. At a macro level, we only see the pandemic in terms of the total/daily number of reported infections, and total/daily number of fatalities. Some of the oldest epidemiological models primarily work with this precise information, and try to model the observations, assuming the reported number of infections is indeed the true number of infections.
Simply put, each individual in the population is assigned a “tag” from a predetermined set of tags, and individuals change their tags at certain rate depending on the interaction between individuals in the population. Modelling the dynamics of how each individual updates her/his tag clearly means having to deal with a large system of coupled equations. Therefore, it becomes challenging to provide analytical estimates for simple statistics like the total number of infections/deaths. Such models are called agent based models.
On the other hand, ignoring the micro (individual) level dynamics, and treating the collection of all individuals with same tags as a single unit represented by the cardinality of the collection, one can model rise/fall in the cardinality of each collection through a set of coupled (stochastic) differential equations. Such models are broadly categorised as compartmental models.
In our effort to understand the underlying dynamics of the ongoing pandemic, we have used simple heuristic models to estimate the number of infected individuals and the fatalities, using two different models.
We do understand that mathematical modelling of epidemics has a long history, and with decades of advancements in the area, we in no way can claim to be subject-matter experts. While the models below are simplistic, and can be interpreted as a first step towards understanding the pandemic. We shall continue to update the models by incorporating finer details.
The information provided here is the result of an academic exercise. The projections are only indicative, and the contributors do not claim that their projections are accurate. The opinions and views expressed here are not endorsed in any shape or form by the organization in which the contributors work.