UNIVERSITA' DI ROMA SAPIENZA FACOLTA' DI FARMACIA E MEDICINA Simulation of the Reed-Frost model for epidemics       The statistical model of epidemics developed in the 1920s by Lowell Reed and Wade Hampton Frost for teaching purposes is both statistically rigorous, elegant and simple.       It is based on the following series of assumptions: an epidemics develops in a community of size N. Each individual is assigned only one of three possible states: S: susceptible; C: affected; I: immune. The state of the individual may change along the irreversible sequence S --> C --> I. Notice that the state "immune" includes all subjects who got the disease and includes those who healed and those who died of it.       The model calculates the probability of each individual to become affected (and successively to become immune) iteratively; each iteration occurs over a time window t corresponding to the average serial generation time of the disease, i.e. the time intercurring between the contagion and the end of infectivity. Every member of the community can encounter every other member and the average number of potentially contagious encounters of each member during the serial generation time t is K. K approximates the maximum possible value of R0 for the epidemy. At the end of the serial generation time the state of the individual changes from C to I.       The probability of a contagious encounter of each individual with another is p = K / (N-1), and the probability that the encounter does not occur is q = 1-p. Disease transimssion occurs if an individual in state C encounters one in state S; the probability for the whole population over one serial time is S * (1-qC). The epidemics ends when the number of individuals in the S state is too low to maintain the transmission.       This interactive simulation assumes that the epidemics occurs in a small village (N from 750 to 1500 individuals) starting from a single case of the disease. you can explore the effect of the population size and of the number of contagious encounters (i.e. the likelyhood of transmission).       Please select the size of the population: 1500 ; 1000 ; 750       Now please select the number of potentially contagious encounters per member of the population (default: 5): 10 ; 5 ; 2 ; 1 . Back to main page.