Illustration of how infection spreads with and without social distanceing and travel restrictions

In this post, we use a cellular automata model of infection to illustrate the effects of social distancing and travel restrictions.

DISCLAIMER:  THIS IS AN UNREALISTIC MODEL, FOR TEACHING PURPOSES ONLY.  IN PARTICULAR THE INFECTION RATIOS ARE PROBABLY TOO SMALL.

The images below are from a cellular automata model of the spread of a disease on a 100x100 grid.  White dots represent uninfected; red dots, infected; green dots, survivors; black dots, deaths.  The key parameters are:

• death rate=1%, given that a person has been infected.  
• r0 = 2 is the basic reproduction number, the number of people infected by each infected person, e.g., here are estimates for corona virus.   We model social distancing as reducing this number.  
• mean distance of infection = 5.0 cells away from an infected cell, modeled as a standard normal distribution over unit distance.  We model travel restrictions as reducing this number

In the video above, the infected cells (red) spread slowly out from the center, where the outbreak began.  Most infections are on the "border" of the infected area because that is where infected cells are more likely to come in contact with uninfected ones.

Infections eventually die out because many of the people who come in contact with the infection have already developed an immunity (green) or are dead (black).  This is referred to as "Herd Immunity."

We graph the spread of the infection below.  The vertical axis represents people on the grid (10,000=100x100) and the horizontal axis represents time, denoted in periods (the life span of an infection virus).   The blue line represents the uninfected population, the green line the infected population, and the orange line, the infection rate.

In the simulation and graph below, we increase r0 (the infection ratio) from 2 to 3, and mean travel distance from 5 to 25.   We see that more people get infected (higher green line), and much more quickly (peak infections occur at period 11, instead of period 15).

What policy makers mean by "flattening the curve" is flattening the orange infection curve (compare the smaller, flatter orange peak in first graph to the  graph to the sharper, higher peak in the second) with social distancing and travel restrictions so that our hospital system does not get overwhelmed by infected patients.

From estimates I have seen, the basic infection ratios for old covid is thought to be around 2.5, but the infection ratio for the new Delta variant is about 3 times as big.  

HT:  Colleague Steven Tschantz designed and wrote the code.