Simulations of Infectious Disease Propagation II, Focusing on Herd Immunity

Introduction and Objectives: 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 as to when the disease’s propagation will dwindle to acceptable levels. 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, 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.

Methods: The method used here was to use computer simulation on a person level to follow the progress of the diseases infection across the population. In the beginning, the people are uniformly distributed in a square. Each person performed a random walk, which simulated the movement of the people. 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 are closer together than a given distance.

Results and Discussion: 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 is 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 were 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.

Conclusions: 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 again 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.