Infectious Disease Epidemiology
and Transmission Dynamics
Ann Burchell
Invited lecture EPIB 695
McGill University
April 3, 2007
Objectives
1)
To understand the major differences between infectious and noninfectious disease epidemiology
2)
To learn about the nature of transmission dynamics and their relevance in
infectious disease epidemiology
3)
Using sexually transmitted infections as an example,
to learn about the key parameters in transmission dynamics
to appreciate the use of mathematical transmission models to assess the
impact of prevention interventions (e.g., vaccines).
Infectious disease epidemiology
Definition of infectious disease (Last, 1995)
“An illness due to a specific infectious agent or its toxic products
that arises through transmission of that agent or its products
from an infected person, animal, or reservoir to a suceptible host,
either directly or indirectly through an intermediate plant or
animal host, vector, or the inanimate environment”
How is infectious disease (ID) epidemiology different
from non-ID epidemiology?
• Prevalence affects incidence, a case can be a
risk factor
– Prevalence not just a measure of burden of disease in a
population, but also the probability of encountering an
infected person
– Means contact patterns between people are critical
• People can be immune
Some key terms to describe individuals
• Susceptible: uninfected, but able to become infected if exposed
• Infectious: infected and able to transmit the infection to other
susceptible individuals
• Immune: possessing cell-mediated or humoral antibody protection
against an infection
• Diseased/clinical infection: implies the presence of clinical signs
of pathology (not synonymous with infected)
• Latent infection / subclinical infection: implies presence of
infectious agent but absence of clinical disease
• Carrier: implies a protracted infected state with shedding of the
infectious agent. Carriers may be diseased, recovering, or healthy.
Key time periods for an infectious disease
Giesecke, J. Modern Infectious Disease Epidemiology. 2002.
Some key terms to describe the
infectious disease at the population level
• Epidemic: The occurrence in a community or region of cases of an
illness clearly in excess of normal expectancy
• Outbreak: An epidemic limited to localized increase in the incidence
of a disease
• Endemic: The constant presence of a disease or infectious agent
within a given geographic area or population group
• Pandemic: An epidemic occurring over a very wide area, crossing
international boundaries and usually affecting a large number of
people
Last, JM. A Dictionary of Epidemiology. 1995.
Examples of transmission routes
Direct transmission
Indirect transmission
Mucous membrane to mucous
membrane – sexually transmitted
diseases
Water-borne – hepatitis A
Across placenta – toxoplasmosis
“Proper” air-borne – chicken pox
Transplants, including blood –
hepatitis B
Food-borne – salmonella
Skin to skin – herpes type I
Vectors – malaria
Sneezes, coughs - influenza
Objects/fomites – scarlet fever
(e.g. toys in a day care centre)
Giesecke J. Modern Infectious Disease Epidemiology. 2002. p. 16
Reproductive rate, R
• Also called “reproductive number”
• Average number of new infections caused by 1 infected
individual
• In an entirely susceptible population
– Basic reproductive rate, R0
• In a population where <100% are susceptible
– Effective reproductive rate, R = proportion susceptible x R0
Basic reproductive rate, R0
R0 > 1 Infection spreads (epidemic)
R0 = 1 Infection remains constant (endemic)
R0 < 1 Infection dies out
Determinants of R0
For a pathogen with direct person-to-person transmission
R0 = βcD
where β is the probability of transmission per contact
between infected and susceptible persons
c is the contact rate
D is the duration of infectivity
Mathematical Model of Transmission Dynamics:
Susceptible-Infectious-Recovered (SIR) model
• Assumptions
–
–
–
–
Population is fixed (no entries/births or departures/deaths)
Latent period is zero
Infectious period = disease duration
After recovery, individuals are immune
• People can be in one of three states
– Susceptible to the infection (S)
– Infected and infectious (I)
– Recovered/immune (R*) * Not to be confused with R
denoting reproductive number…
unfortunate nomenclature!
Giesecke J. Modern Infectious Disease Epidemiology. 2002. pp. 126-130
Rate of change
Proportion in state at time t
1 OUT
Susceptible
dS/dt = - βcSI
St = St-1 - βcSt-1It-1
(S)
1
1 IN
Infected
2 OUT
dI/dt = + βcSI – I/D
It = It-1 + βcSt-1It-1 – It-1/D
(I)
2
2 IN
Recovered
(R)
dR/dt = + I/D
Rt = Rt-1 + It-1/D
Example SIR Model
• Consider the following values
–
–
–
–
N = 1000 people
Transmission probability, β = 0.15
Contact rate, c = 12 contacts per week
Infection duration, D = 1 week
• Basic reproductive rate: R0 = 0.15 * 12 * 1 = 1.8
• Effective reproductive rate at time t: Rt = St * R0
Mathematical Models of Infectious
Disease Transmission Dynamics
• Frequently used in infectious disease epidemiology
• Major goal is to “further understanding of the interplay
between the variables that determine the course of
infection within an individual, and the variables that
control the pattern of infection within communities of
people”
Anderson RM & May RM. Infectious Diseases of Humans.
Dynamics and Control. 1991.
Why develop a model?
• To understand the system of transmission of infections in
a population
• To help interpret observed epidemiological trends
• To identify key determinants of epidemics
• To guide the collection of data
• To forecast the future direction of an epidemic
• To evaluate the potential impact of an intervention
Types of transmission models
• Deterministic/compartmental
– SIR model example
– Categorize individuals into broad subgroups or “compartments”
– Describe transitions between compartments by applying average
transition rates
– Aim to describe what happens “on average” in a population
– Results imply epidemic will always take same course
• Probabilistic/stochastic (Monte Carlo, Markov Chain)
– Incorporates role of chance and variation in parameters
– Provides range of possible outcomes
– Particularly relevant for small populations and early in epidemic
• Main challenge for both types of models? Good data for
transmission parameters!
Sources of data for model parameters:
The example of sexually transmitted infections (STI)
• Recall the three main parameters are:
– Transmissibility (β)
– Duration of infectivity (D)
– Contact rate (c)
• Where do estimates of these parameters come from?
β
Anderson RM. Transmission dynamics of sexually transmitted infections. In: Sexually
Transmitted Diseases. Holmes KK et al., eds. 1999. pp. 25-37
Transmissibility (β): Measurement
• Measured as the probability of transmission from an
infected to a susceptible partner (attack rate)
• Sources of data
– Contact tracing
– Discordant couples
– Studies of sexually active individuals who report partners with
known STI status, or if the prevalence of the STI in the pool of
partners is well known
• Challenges
– Enrollment of sexual partners may be difficult
– Identification of contacts between infected and susceptibles, and
direction of transmission
– What is a “contact”?
Duration of infectivity (D): Measurement
• Sources of data
– Duration of clinical disease
– Duration of infection
• Challenges in measurement
–
–
–
–
Duration of disease = duration of infectivity?
Asymptomatic versus symptomatic
Ethical obligation to treat identified infections
May need to rely on historical data of questionable quality
Contact rate (c)
• Typically measured as the rate of new partner acquisition
(e.g., per year)
• Model so far assumes homogeneity in contact rate
• Data source is sexual behaviour surveys
– General population
– Selected populations (e.g., adolescents, adults aged 18-45,
students, gay and bisexual men, drug users)
Number of partners in past 5 years. British National Survey
of Sexual Attitudes and Lifestyles (NATSAL), 2000
Female
Male
60
Percentage
50
40
30
20
10
0
0
1
2
Johnson AM et al. Lancet 2001; 358:1835-42.
3 to 4
5 to 9
10 or
more
Contact rate (c)
• Clearly, the contact rate is heterogeneous
• One cannot assume that all individuals have the same
contact rate
• For sexual behaviour, an important concept is the “core
group”
– A small group of individuals with a high contact rate that
contribute disproportionately to the spread of STIs in the
population
– STI becomes concentrated in this core group
Random mixing and the contact rate (c)
• An assumption of the simple models seen so far is that
mixing is random
• Every individual has an equal chance of forming a
partnership with every other individual
• Survey data show that mixing is not random for many
characteristics (e.g., age, ethnicity, religion, education),
but tends to be assortative
– “Like” mix with “like”
• But is mixing assortative with respect to past sexual
history (and by extension, the likelihood of STI
infection)?
Partner choice and sexual mixing
Anderson RM. 1999.
Contact rate (c): measurement challenges
• Surveys of individuals obtain data on their sexual
behaviour, but will be incomplete for their partners
• Sexual network studies get detailed partner data, but are
usually localized and may not be generalizable
• General population surveys are more representative of
majority, but may insufficiently capture members of the
core group
• Validity of self-reported sexual behaviour and social
desirability bias
β, c, and D estimates: Bottom line
• Uncertainty and limitations in parameter estimates
• Well-written papers will
– Identify the source or reasoning behind parameter estimates
– Conduct sensitivity analysis to determine how much the model
results depend on parameter values
• Sometimes the transmission model will identify a lack of
knowledge in these parameters, and can direct empirical
research to obtain more data
Example of a mathematical
transmission model to assess
the impact of a prevention
intervention
Hughes JP, Garnett GP, Koutsky L. The
theoretical population-level impact of a
prophylactic human papillomavirus vaccine.
Epidemiology 2002; 13:631-639
Human papillomavirus (HPV)
• Over 40 types of HPV infect the epithelial lining of the
anogenital tract
• Some can lead to cancer of the cervix, and may also
cause cancers of the vagina, penis, or anus (high-risk
oncogenic types)
• Some produce genital warts (low-risk types)
Epidemiology of HPV
• HPV present in 5%-40% of asymptomatic women of
reproductive age
• As many as 75% of adults are thought to be infected
with at least one HPV type in their lifetime
• For the vast majority, the infection causes no ill health
effects and is cleared within 1-2 years
• Among women in whom HPV infection persists, time
from initial infection to cervical cancer thought to be
10-15 years
Worldwide Distribution of Cervical
Cancer, 2002
Canada '05
Morbidity
7.6 per 100,000
Mortality
2.0 per 100,000
Rate per 100,000 women
Vaccine to prevent cancer!
• Gardasil™ by Merck
– Protects against infection with HPV-16 and HPV-18, as well
as HPV-6 and HPV-11, the types that cause most genital
warts
– Vaccine efficacy 89%+ (Villa et al., 2005)
– Approved for use in girls and women aged 9-26 in Canada
• Cervarix™ by GlaxoSmithKline
– Protects against infection with HPV-16 and HPV-18, the types
that cause most cervical cancers
– Division of Cancer Epidemiology, McGill University involved
in design & data analysis of trial
– Vaccine efficacy 83%+ (Harper, Franco et al., 2004)
Hughes JP et a. The theoretical population-level impact
of a prophylactic human papilloma virus vaccine.
Epidemiology 2002; 13:631-9.
• Model 1 is a compartmental model of HPV transmission
dynamics
• Sexually active population, which authors implicitly
defined as having contact rate c > 0 (i.e., acquiring new
partners over time)
• Vaccine benefits: ↓ susceptibility, ↓ transmissibility,
duration of infectiousness
• Vaccine failure: take, degree, duration
↓
μ
Sexually active population (η)
Φ
μ
Vaccinated (v)
1-Φ
μ
σ
Susceptible (x)
φλ
μ
λ
Infected (w)
Infected (y)
γ
αγ
Recovered,
immune (z)
μ
Hughes JP et al. Epidemiology 2002; 13:631-9.
μ
β, D, and c parameter estimates
• Transmissibility (β)
– Female-to-male = 0.7
– Male-to-female = 0.8
• Duration of infectiousness (D)
– 1.5 years
• Contact rate (c)
– High activity class: 3% of population, 9.0 new partners per year
– Medium activity class: 15% of pop, 3.0 new partners per year
– Low activity class: 82% of pop, 1.4 new partners per year
– Mixing parameter, ε = 0.7, where ε = 1 is fully random, and ε = 0
is fully assortative
Hughes JP et al. Epidemiology 2002; 13:631-9.
%
reduction
--44%
68%
30%
19%
12%
* 90% vaccine coverage, 75% vaccine efficacy, 10-year protection, similar natural history
† 90% vaccine coverage in high and medium sexual activity class, 10% coverage in low
sexual activity class
Hughes JP et al. Epidemiology 2002; 13:631-9.
Hughes JP et al. Epidemiology 2002; 13:631-9.
Hughes et al - Conclusions
• Given assumptions, an HPV vaccine for a given type
would reduce prevalence of that type by
– 44% if females and males vaccinated
– 30% if only females vaccinated
• Over a broad range of assumptions, female-only
vaccination would be 60%-75% as effective as a strategy
which vaccinated both females and males
• Vaccination targetted to high-risk individuals only would
reduce prevalence by no more than 19%, probably less
given difficulty in reaching these individuals
Hughes JP et al. Epidemiology 2002; 13:631-9.