Transcript Epidemiology modeling with Stella

Epidemiology modeling
with Stella
CSCI 1210
Stochastic vs. deterministic



Suppose there are 1000
individuals and each one
has a 30% chance of
being infected:
Stochastic method: run
the model on the right
1000 times
Deterministic method:
1000 * 30% = 300 get
infected
(Law of Mass Action)
Stella Stocks and Flows
takes “stuff” out from a stock or
puts stuff into a stock
 A flow
Result of simple flow model
Simple Epidemic Flow models
 A short-term
illness with recovery and
permanent immunity
Simple Epidemic Flow Models
 Short-term
lethal illness with no recovery
or immunity
 Examples: “Martian flu”, measles in Incas
 Note the flow into a sink outside the model
Simple Epidemic Flow Models
 Short-term
illness with recovery and
temporary immunity
 Example: malaria
Filling out the model
 These
are dynamic models
 The value of each stock depends only on
the initial value and the flows over time
 The flows depend on the assumptions and
state of the model – this is what
determines how the model works
The Infection process
 Simplest
model: small population in which
everyone is in contact
 Each sick person has a certain constant
probability of infecting each susceptible
person in one time unit
 Size of infection flow depends on the
number of sick people and the number of
susceptibles.
Modeling infection in Stella

The thin arrows represent influences. Note that
all the influences affect the rate of infection.
 We leave out incubation for simplicity: everyone
is either susceptible or ill.
Qualitative analysis of infection
 When
there are few sick people, there can
be little infection
 When nearly everyone is sick, there can
be little infection
 Maximum infection will occur when the
population is between these cases
 Eventually, everyone will get sick.
Results of simple SI model
Results of simple SI model
A model with recovery and
immunity

After recovery, people are neither susceptible
nor ill
 A certain fraction of ill people will recover
each time period.
 The rate of recoveries depends on the
number of ill people.
Results of the SIS model
Infection and recovery rates
Effect of immunization
 Reduces
the initial number of susceptibles
 This reduces the infection rate, but does
not alter the recovery rate
 If the infection rate is small enough, the
disease will die out without becoming an
epidemic (herd immunity).
Infection and recovery, with herd
immunity
Results of immunization
campaign
Notes on Herd immunity
 Not
necessary to vaccinate the entire
population.
 Even individuals who were not vaccinated
share the benefits.
HIV
 Human
Immunodiciency Virus (HIV)
 A retrovirus
 Originated in Africa, probably in 20th
century
 Descended from simian virus (SIV) which
“jumped hosts”
 Long, contagious incubation period
From HIV to AIDS
 Virus
attacks human immune system
 Death is from opportunistic secondary
infections, not HIV itself
 Anti-retroviral drugs can slow the virus and
prolong life.
AIDS and Africa
 42
million HIV/AIDS cases worldwide
 29 million cases in Africa
 Origin of the virus
 Anarchy in central Africa (Uganda,
Rwanda, Congo) helps spread the disease
AIDS: the “Gay Plague”?
 Initially,
US AIDS cases were almost all in
gay men
 However, African AIDS cases are mostly
heterosexual
 More US heterosexual AIDS cases as time
has passed
 What gives?
A two-tier model
 High-risk
group initially contracts the
disease
 Low-risk group does not have the disease
 Slight interaction between groups
 Two submodels proceed separately but
have a weak coupling
Two-tier model
Results of the two-tier model
AIDS and the “Martian Flu”
 HIV/AIDS
is incurable, fatal, and has no
known immunity
 However, US AIDS epidemic may have
peaked
 So, “Martian Flu” model needs elaboration
Elaborated AIDS model
 Add
birth and death flows for susceptibles
who do not get infected
 Either die naturally, retire from sex, or
enter monogamous relationships
 Creates a situation similar to “herd
immunity” model
Elaborated single-pool model
AIDS model with high riskiness
AIDS model with low riskiness