Simulations of Infectious Disease Propagation II: Herd Immunity Examined

The results of simulations of the propagation of an infectious disease are presented. In managing and controlling the spread of an infectious disease, such as Covid-19, the concept of “Herd Immunity” (HI) is often invoked when the disease’s propagation will dwindle to acceptable level. We have extended a previous work with explicit attention on the usefulness of this concept. The objectives of this research was to track the propagation of an infectious disease as a function of population density and time and to evaluate HI. The population was divided into two groups. One group was protected from the infection. The second group was unprotected. The results are given as a percentage of the unprotected population that is infected as a function of time. We used computer simulation on a person level to follow the progress of the disease’s infection across the population. In the beginning, the people are uniformly distributed in a square. Movement of the people was simulated by each person performing a random walk. Infection rates are given for the unprotected portion of the population as a function of time. The disease was transferred from an infected person to an uninfected person if the two people were closer together than a given distance. These simulations show the unprotected portion of the population was at total risk if proper measures are not taken early. For 400 unprotected people the infection rate was 100% after approximately 100,000 iterations. We give the results from one dual simulation in which protection was afforded for a significant part of the population and carried out until all of the unprotected were infected. In the second part the protection was lifted to see how fast the total population was infected. For the case of 50% protected it took 400,000 iterations to infect the unprotected people. After the restrictions were lifted it took 150,000 to infect the other half. The simulations here are people based which has the advantage of seeing individual personal involvement. Results of infection rates were calculated for 1,000, 2,500, 5,000, and 10,000 people. The propagation of the disease can be fast and depends on population density. Protection is vital to containing the disease. Restrictions must be lifted carefully and slowly or the total population is at risk. According to the results obtained here the concept of HI is not a viable concept in controlling or managing the spread of the disease. We also present some data on how many people one person infected during the simulation.