Simplified Epidemiological Model
The parameters used to create the graph shown below are the
following (these can be modified as desired, as long as the values
are non-negative numbers, with Xmax a
positive integer):
- Xmax — the length of the X axis
in units of days. This value must be an integer.
- Ymax — the length of the Y axis
as a count of the number that is infectious.
- N — the size of the population.
- NE0 — the initial number that
was exposed but not yet infectious.
- NI0 — the initial number that
is infectious.
- R0 — the basic reproduction number
(the average number each infectious individual would infect if no one
else were infected). The behavior is very sensitive to this number and
it can be modified by changing human behavior for instance using a
mask to reduce the number of infections).
- τE — the length of the exposed
period in days.
- τI — the length of the infectious
period in days.
The black line shows the number of individuals who are infectious as
function of time. The blue line shows the percentage of the
population that is not susceptible. The right axis (i.e., the blue
axis) goes from 0% to 100%.
Parameters | Graph |
|
|
The graphs were produced by solving the following system of first-order
differential equations:
- n′E = -nE/τE + (R0/τI)nI(1 - n/N)
- n′I = nE/τE - nI/τI
- n′ = (R0/τI)nI(1 - n/N)
where
- nE is the number who are exposed
and infected but not yet infectious at each point in time.
- nI is the number who are
infectious at each point in time. This value as a function of
time is shown on the graph by the black curve.
- n is the cumulative number of cases
including those currently infected and those who have
recovered and are hence immune. This value as a function of
time is shown on the graph by the blue curve.