Simulation of the Transmission and Control of Infectious Disease - SEIR Model and its Generalization
Project for Mathematical Structures of Complex Systems, Heidelberg University, WS 2019/2020
by Rui Wang
Compartmental models divide a population into compartments (or groups) based on individual’s health status and track the corresponding population size through time. Each compartment represents a group of individuals in the same health state. The connections between compartments indicate the direction and rate of movement from one health state to another.
Let’s consider SIR model. We make the following hypotheses about the transmission process of an infectious disease and its host population:
(1) Transmission occurs horizontally through direct contact between hosts.
(2) Mixing of individual hosts is homogeneous and thus the Law of Mass Action holds: the number of contacts between hosts from different compartments depends only on the number of hosts in each compartment.
(3) Rate of transfer from a compartment is proportional to the population size of the compartment.
(4) Infected individuals become infectious upon infection with no latency period.
(5) The immunity is permanent and it’s not possible to be re-infected.
(6) Ignore demography, i.e. natural birth rate and mortality.
(7) The total population remains a constant.