A re-examination of models of epidemics

We develop models to predict the unfolding of events. Models in turn guide our responses to the unfolding of events. In the current pandemics of novel coronavirus disease, many governments adopt the policy of “herd immunity”. We attempt to "flatten the curve". It is to slow down the speed of infection. This is also to acknowledge, at least implicitly, we can do little to influence the total number of infections. We reach this conclusion based on the mathematical models of epidemics. But how accurate do these models describe the process of infection?

One type of popular models on epidemics is called SIR models. S, I, and R each represents a segment of the population. S represents the susceptible. I represents the infected. R represents the recovered, or removed.  The SIR model consists of three ordinary differential equations, each representing the rate of change of S, I, or R.  In the standard SIR model, we can adjust behaviors to "flatten the curve". But we can do relatively little to change the total number of infections. This is the theoretical foundation for the policy of “herd immunity”, which let every susceptible get infected and hopefully get recovered, (or removed, i.e., dead).

Does the model capture the main factors in epidemics? One of the most important factors in epidemics is the total number of infected. Many public media trace this number constantly and many people pay close attention to this number. However, this number does not appear in the SIR model. In SIR model, I represents the number of currently being infected, not the total infection number. With higher total infection number, more people and organizations adjust their behaviors. This will affect the rate of infection. When we put the total infection number into the model, the predicted results will change as well. In particular, not all or most susceptible have to be infected before the pandemics runs its course. If most individuals and institutions can adopt strong enough response, the pandemics can be stopped early on. Indeed, most infectious diseases do not infect majority of the population. Our behaviors not only affect the shape of the infection curve, but also the total infection number.

Other than SIR models, some simulations also explore the possible outcomes of epidemics. These simulations and other intuitive arguments suggest that our behaviors can not only flatten the curve, but also change the total number of infections. However, the dominant academic opinion seems to be that the majority of the population will be infected. This theory is presented as “science”. This theory forms the foundation of policies for many governments. There is no such thing as “science”. What we called “science” is usually the most established academic theories. Since the establishment of the SIR models, there has been no global public response as strong as the current coronavirus pandemic. Theories adequate enough in the past may not be able to represent the current situation. In this time of critical moment, we especially need to re-examine the foundation of the dominant theories that greatly influence our policies. It could save a lot of lives.

For detailed discussion on the mathematical models, please check

https://www.researchgate.net/publication/340309946_A_re-examination_of_models_of_epidemics