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Objectives. To understand the major differences between infectious and non-infectious disease epidemiologyTo learn about the nature of transmission dynamics and their relevance in infectious disease epidemiologyUsing sexually transmitted infections as an example,to learn about the key parameters
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1. Infectious Disease Epidemiology and Transmission Dynamics Ann Burchell
Invited lecture EPIB 695
McGill University
April 3, 2007
2. Objectives To understand the major differences between infectious and non-infectious disease epidemiology
To learn about the nature of transmission dynamics and their relevance in infectious disease epidemiology
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).
3. 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”
4. 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
5. 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.
6. Key time periods for an infectious disease Incubation period: extends from the moment a person is infected until they develop symptoms of disease
Serial interval (or generation time): for diseases that are spread person-to-person, it is the time period between the appearance of symptoms in successive generations
Infectious period: time period during which a person can transmit the infection
Latent period: time period from infection until the infectious period startsIncubation period: extends from the moment a person is infected until they develop symptoms of disease
Serial interval (or generation time): for diseases that are spread person-to-person, it is the time period between the appearance of symptoms in successive generations
Infectious period: time period during which a person can transmit the infection
Latent period: time period from infection until the infectious period starts
7. 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
8. Examples of transmission routes
9. 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
10. Basic reproductive rate, R0
R0 > 1 Infection spreads (epidemic)
R0 = 1 Infection remains constant (endemic)
R0 < 1 Infection dies out
11. Determinants of R0 For a pathogen with direct person-to-person transmission
R0 = ßcD
where ß is the probability of transmission per contact between infected and susceptible persons
c is the contact rate
D is the duration of infectivity
What examples of factors affecting these 3 components can you think of?
Some examples…
ß: handwashing, condoms, face masks, sterilization of medical instruments, weakened immunity (e.g. due to age, other illness, immunosuppressive drugs)
c: population density (urban/rural, schools, daycares, nursing homes), quarantine
D: treatmentWhat examples of factors affecting these 3 components can you think of?
Some examples…
ß: handwashing, condoms, face masks, sterilization of medical instruments, weakened immunity (e.g. due to age, other illness, immunosuppressive drugs)
c: population density (urban/rural, schools, daycares, nursing homes), quarantine
D: treatment
12. 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*)
14. Example SIR Model Consider the following values
N = 1000 people
Transmission probability, ß = 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 Go to Excel spreadsheet “SIR Model.xls” Go to Excel spreadsheet “SIR Model.xls”
15. 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”
16. 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
17. 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!
18. Sources of data for model parameters: The example of sexually transmitted infections (STI) Recall the three main parameters are:
Transmissibility (ß)
Duration of infectivity (D)
Contact rate (c)
Where do estimates of these parameters come from?
20. Transmissibility (ß): 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”?
21. 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
22. 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)
23. Number of partners in past 5 years. British National Survey of Sexual Attitudes and Lifestyles (NATSAL), 2000
24. 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
25. 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)?
26. Partner choice and sexual mixing
27. 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
28. ß, 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
29. 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 Refer to handout.Refer to handout.
30. 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) There are over 40 sexually-transmitted HPV types.
Those that can lead to cancer are called “high-risk oncogenic types”. They can cause cervical cancer, but also vaginal, penile, and anal cancers.
Those HPV types that don’t lead to cancer are called “low-risk types”. These may produce genital warts.There are over 40 sexually-transmitted HPV types.
Those that can lead to cancer are called “high-risk oncogenic types”. They can cause cervical cancer, but also vaginal, penile, and anal cancers.
Those HPV types that don’t lead to cancer are called “low-risk types”. These may produce genital warts.
31. 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 HPV is the most common STI, with prevalence estimated between 5-40% depending on the study.
In fact, as many as 3 in 4 adults are thought to have an HPV infection at least once in their lifetime.
For most women, HPV infections are of little consequence. They are asymptomatic and clear within about one year.
However, among some women these infections persist, and result in an increased risk for cervical cancer.HPV is the most common STI, with prevalence estimated between 5-40% depending on the study.
In fact, as many as 3 in 4 adults are thought to have an HPV infection at least once in their lifetime.
For most women, HPV infections are of little consequence. They are asymptomatic and clear within about one year.
However, among some women these infections persist, and result in an increased risk for cervical cancer.
32. Worldwide Distribution of Cervical Cancer, 2002 Worldwide, cervical cancer is the 2nd leading cancer site among women.
This figure gives you a sense of the geographical distribution of the rates of new diagnoses of cervical cancer.
Countries with the highest incidence of cervical cancer, shown in red, are in sub-Saharan Africa, South America, and some parts of Asia.
Countries with the lowest incidence are shown in dark green, and Canada is among them. In 2005, the rate of new cervical cancer diagnoses was just under 8 per 100,000 women, with low mortality, and cervical cancer was the 12th most common cancer. These low rates are attributed to Pap test screening programs in Canada, and as well to low fertility rates. Nevertheless, about 400 Canadian women die of cervical cancer per year.Worldwide, cervical cancer is the 2nd leading cancer site among women.
This figure gives you a sense of the geographical distribution of the rates of new diagnoses of cervical cancer.
Countries with the highest incidence of cervical cancer, shown in red, are in sub-Saharan Africa, South America, and some parts of Asia.
Countries with the lowest incidence are shown in dark green, and Canada is among them. In 2005, the rate of new cervical cancer diagnoses was just under 8 per 100,000 women, with low mortality, and cervical cancer was the 12th most common cancer. These low rates are attributed to Pap test screening programs in Canada, and as well to low fertility rates. Nevertheless, about 400 Canadian women die of cervical cancer per year.
33. 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)
Cervical cancer research is quite exciting these days, because we now have a vaccine to prevent cancer!
Two vaccines have been developed. Clinical data indicate that they offer excellent protection against HPV infection. One vaccine, Gardasil, has been approved in Canada, and the second, Cervarix, is expected to be approved soon.
But there is much to work out regarding the most appropriate and cost-effective vaccine strategy after licensure. Mathematical models can help us to anticipate the impact of a particular strategy.
Cervical cancer research is quite exciting these days, because we now have a vaccine to prevent cancer!
Two vaccines have been developed. Clinical data indicate that they offer excellent protection against HPV infection. One vaccine, Gardasil, has been approved in Canada, and the second, Cervarix, is expected to be approved soon.
But there is much to work out regarding the most appropriate and cost-effective vaccine strategy after licensure. Mathematical models can help us to anticipate the impact of a particular strategy.
34. 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
Compartmental model (as opposed to stochastic) ? dealing with population averages.
The model concerns the sexually active population, which the authors do not explicitly define, but imply that this consists only of individuals who are acquiring new partners.
In their modeling, they explore 3 potential benefits of vaccination:
Decreased susceptibility
Decreased transmissibility in breakthrough infections
Decreased duration of infectiousness in breakthrough infections
The model allows for 3 types of vaccine failures:
Take (when the vaccine has no effect in some people)
Degree (when the vaccine reduces but does not eliminate susceptibility)
Duration (loss of protective immunity over time)
Compartmental model (as opposed to stochastic) ? dealing with population averages.
The model concerns the sexually active population, which the authors do not explicitly define, but imply that this consists only of individuals who are acquiring new partners.
In their modeling, they explore 3 potential benefits of vaccination:
Decreased susceptibility
Decreased transmissibility in breakthrough infections
Decreased duration of infectiousness in breakthrough infections
The model allows for 3 types of vaccine failures:
Take (when the vaccine has no effect in some people)
Degree (when the vaccine reduces but does not eliminate susceptibility)
Duration (loss of protective immunity over time)
35. People enter and exit the sexually active population at a constant rate µ (MU), where 1/µ is the mean duration in the sexually active population in years.
A proportion F (upper-case PHI) of the sexually active population is vaccinated and successfully immunized. This incorporates vaccine “take”.
A proportion s (SIGMA) lose their protective immunity over time and enter the Susceptible compartment, where 1/s is the duration of vaccine protection.
Susceptibles are infected with HPV-16 at a constant rate ? (LAMBDA), otherwise known as the “force of infection”.
Immunized individuals are also infected with HPV-16 at rate f?, where f (lower-case PHI) is the susceptibility of immunized individuals relative to unimmunized individuals (i.e. f is a relative risk). If the vaccine is 100% effective, then f is 0 and no immunized individuals become infected. If the vaccine efficacy is less than 100%, then some immunized individuals will have “breakthrough” infections.
Infected individuals recover and become immune at rate ? (GAMMA), where 1/? is the mean duration of infectiousness.
Immunized individuals with breakthrough infections recover at rate a?, where a (ALPHA) is the relative rate of recovery from infection in immunized versus unimmunized invididuals. People enter and exit the sexually active population at a constant rate µ (MU), where 1/µ is the mean duration in the sexually active population in years.
A proportion F (upper-case PHI) of the sexually active population is vaccinated and successfully immunized. This incorporates vaccine “take”.
A proportion s (SIGMA) lose their protective immunity over time and enter the Susceptible compartment, where 1/s is the duration of vaccine protection.
Susceptibles are infected with HPV-16 at a constant rate ? (LAMBDA), otherwise known as the “force of infection”.
Immunized individuals are also infected with HPV-16 at rate f?, where f (lower-case PHI) is the susceptibility of immunized individuals relative to unimmunized individuals (i.e. f is a relative risk). If the vaccine is 100% effective, then f is 0 and no immunized individuals become infected. If the vaccine efficacy is less than 100%, then some immunized individuals will have “breakthrough” infections.
Infected individuals recover and become immune at rate ? (GAMMA), where 1/? is the mean duration of infectiousness.
Immunized individuals with breakthrough infections recover at rate a?, where a (ALPHA) is the relative rate of recovery from infection in immunized versus unimmunized invididuals.
36. ß, D, and c parameter estimates Transmissibility (ß)
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, e = 0.7, where e = 1 is fully random, and e = 0 is fully assortative Although it is not explicitly stated, one assumption throughout this paper is that all sexual activity is heterosexual.Although it is not explicitly stated, one assumption throughout this paper is that all sexual activity is heterosexual.
37. Assumptions:
90% vaccine coverage
Vaccine reduces infection by 75%
Vaccine confers 10 year protection
Breakthrough infections have similar natural history to infections in unvaccinated individuals
In “targetted” approach, coverage is 90% in two highest risk groups, 10% in lowest risk group
Authors conclude that vaccinating women only would be a reasonable strategy, since it would achieve 68% of the reduction in HPV-16 prevalence in women.
Conversely, the targetted approach would be less effective.
Assumptions:
90% vaccine coverage
Vaccine reduces infection by 75%
Vaccine confers 10 year protection
Breakthrough infections have similar natural history to infections in unvaccinated individuals
In “targetted” approach, coverage is 90% in two highest risk groups, 10% in lowest risk group
Authors conclude that vaccinating women only would be a reasonable strategy, since it would achieve 68% of the reduction in HPV-16 prevalence in women.
Conversely, the targetted approach would be less effective.
38. Main result in this table is the relative reduction in female HPV-16 prevalence, comparing female only to male&female vaccine strategies.
1/µ = mean duration in the “sexually active population
e = mixing parameter, where 0 is fully assortative and 1 is random
c = contact rate ? greatest variability in vaccine impact, as it varies from 0.639 to 0.732 with contact rate, such that lower heterogeneity in contact rates result in poorer impact of female only strategy compared to higher heterogeneity
r = relative risk of transmission in breakthrough vs unvaccinated infectionsf =relative susceptibility of vaccined to unvaccinated individuals 1/s = mean duration of vaccine protection
a = relative rate of recovery of breakthrough vs unvaccinated infections
F = proportion who are effectively vaccinated (includes “take”)
TAKE HOME MESSAGE: over broad range of assumptions, female only vaccination strategy is 60%-75% as good as vaccinated both females and males
Main result in this table is the relative reduction in female HPV-16 prevalence, comparing female only to male&female vaccine strategies.
1/µ = mean duration in the “sexually active population
e = mixing parameter, where 0 is fully assortative and 1 is random
c = contact rate ? greatest variability in vaccine impact, as it varies from 0.639 to 0.732 with contact rate, such that lower heterogeneity in contact rates result in poorer impact of female only strategy compared to higher heterogeneity
r = relative risk of transmission in breakthrough vs unvaccinated infectionsf =relative susceptibility of vaccined to unvaccinated individuals 1/s = mean duration of vaccine protection
a = relative rate of recovery of breakthrough vs unvaccinated infections
F = proportion who are effectively vaccinated (includes “take”)
TAKE HOME MESSAGE: over broad range of assumptions, female only vaccination strategy is 60%-75% as good as vaccinated both females and males
39. 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