Infectious Disease Epidemiology and Transmission Dynamics Ann Burchell Invited lecture EPIB 695 McGill University April 3, 2007

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).

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”

Prevalence affects incidence, a case can be a risk factor 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 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 starts 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 What examples of factors affecting these 3 components can you think of? Some examples… β: 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

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

Susceptible (S) Infected (I) Recovered (R) Rate of change Proportion in state at time t dS/dt = - βcSI 1 OUT Susceptible (S) St = St-1 - βcSt-1It-1 It = It-1 + βcSt-1It-1 – It-1/D Rt = Rt-1 + It-1/D 1 dI/dt = + βcSI – I/D 1 IN 2 OUT Infected (I) 2 dR/dt = + I/D 2 IN Recovered (R)

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 Go to Excel spreadsheet “SIR Model.xls”

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 Number of partners in past 5 years. British National Survey of Sexual Attitudes and Lifestyles (NATSAL), 2000 Johnson AM et al. Lancet 2001; 358:1835-42.

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 Refer to handout.

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.

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.

Worldwide Distribution of Cervical Cancer, 2002 Canada '05 Morbidity 7.6 per 100,000 Mortality 2.0 per 100,000 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. 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) 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.

Model 1 is a compartmental model of HPV transmission dynamics 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)

Sexually active population (η) μ Sexually active population (η) Φ 1 - Φ μ μ σ Vaccinated (v) Susceptible (x) φλ λ μ μ Infected (w) Infected (y) 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 Φ (upper-case PHI) of the sexually active population is vaccinated and successfully immunized. This incorporates vaccine “take”. A proportion σ (SIGMA) lose their protective immunity over time and enter the Susceptible compartment, where 1/σ is the duration of vaccine protection. Susceptibles are infected with HPV-16 at a constant rate λ (LAMBDA), otherwise known as the “force of infection”. Immunized individuals are also infected with HPV-16 at rate φλ, where φ (lower-case PHI) is the susceptibility of immunized individuals relative to unimmunized individuals (i.e. φ is a relative risk). If the vaccine is 100% effective, then φ 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 γ (GAMMA), where 1/γ is the mean duration of infectiousness. Immunized individuals with breakthrough infections recover at rate αγ, where α (ALPHA) is the relative rate of recovery from infection in immunized versus unimmunized invididuals. αγ γ Recovered, immune (z) μ Hughes JP et al. Epidemiology 2002; 13:631-9.

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 Although it is not explicitly stated, one assumption throughout this paper is that all sexual activity is heterosexual. Hughes JP et al. Epidemiology 2002; 13:631-9.

% reduction --- 44% 30% 19% 12% 68% 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. * 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. 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 ε = 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 infectionsφ =relative susceptibility of vaccined to unvaccinated individuals 1/σ = mean duration of vaccine protection α = relative rate of recovery of breakthrough vs unvaccinated infections Φ = 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 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.