Lecture 3 Epidemiology of Infectious Diseases PDF

Lecture 3: Epidemiology of Infectious diseases Marina Treskova, PhD Head of Research Group Eco-Epidemiology Heidelberg Institute of Global Health &...

Lecture 3: Epidemiology of Infectious diseases Marina Treskova, PhD Head of Research Group Eco-Epidemiology Heidelberg Institute of Global Health & Interdisciplinary Centre for Scientific Computing Heidelberg University www.hei-planet.com 01/15/2025 Outline Infectious Diseases and Public Health Foundations of infectious diseases Endemic, epidemic, and pandemics Modeling epidemics 01/15/2025 Infectious Diseases are caused by micro-organisms: viruses, bacteria, parasites, fungi, prions are transmitted to humans from other humans, insects, animals or the environment usually follow a patterns of symptoms, timing – natural history. change over time as agents evolve and new organisms emerge due to human behavior and environments change (Land use, climate change) 01/15/2025 Infectious Disease Epidemiology: specifics Epidemiology of ID: Addresses biology and patterns of specific ID Studies transmission patterns and distribution of risks via understanding of interactions, drivers and processes Small-scale investigations: outbreaks -“shoe leather” epidemiology Population-level disease dynamics via mathematical models for: Surveillance Prevention Control Source: Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Infectious Diseases: terminology Endemic: The habitual presence of a disease within a given geographic area; may also refer to the usual prevalence of a given disease within such an area. Epidemic: The occurrence in a community or region of a group of illnesses of similar nature, clearly in excess of normal expectancy, and derived from a common or from a propagated source. Pandemic: A worldwide epidemic. Zoonosis: An infection or an infectious disease transmissible under natural conditions between vertebrate animals and man Enzootic: “Endemic” among animal populations Epizootic: “Epidemic” among animal populations Spillover: cross-species transmission of pathogen, where recipient host is a dead- end host 01/15/2025 Infectious Diseases: terminology Infectious Disease agent All three of these are constantly changing: Disease agent: Microorganisms adapt to changing conditions, including human control efforts such as antibiotics. Dynamic Host: Human and animal populations are interaction constantly growing and moving into new environments. Host Environment Environment: Changes occur locally and Sex Factors influencing globally, both naturally and through human intervention. Race Age agent’s survival and Occupation growth, and a host’s Nutrition contact with a disease Heredity agent: Marital status Temperature, pollution, Socioeconomic status Water, … Religious and social customs Immunization history Previous history of disease 01/15/2025 Infectious disease: from exposure to disease Infectious process: Exposure: a person is placed in a situation where effective transmission of an infectious agent could occur. Does not mean transmission Colonization: is the presence of a microorganism in or on a host with growth and multiplication but without any overt clinical expression or immune reaction in the host Infection: replication of infectious disease agent in human/animal body depending on cell type and the agent Asymptomatic: no symptoms are visible Symptomatic: clinical symptoms are shown Recovery or death 01/15/2025 Infectious disease transmission: reservoirs, vector, vehicle Reservoir: any person, animal, plant, or environmental medium (soil, water) in which the microorganism normally lives and multiplies, on which it depends primarily for survival, and where it reproduces itself in such a manner that it can be transmitted to the susceptible host (S. Straif-Bourgeois et al. ) Human reservoirs: acute clinical cases and carriers Incubatory carriers Inapparent infections (also called subclinical cases) Convalescent carriers - continue to be infectious during and even after their recovery from illness Chronic carriers: people who continue to harbor infections for a year or longer after their recovery Animal Reservoirs: acute clinical cases and carriers Environmental Reservoirs: Plants, soil and water may serve as the reservoir of infection for a variety of diseases (e.g. fungi) Vehicle: an inanimate object which serves to communicate disease, for example, a glass of water containing microbes or a dirty rag. Vector: a live organism that serves to communicate disease – mosquitoes, flies, ticks. 01/15/2025 Transmission: portals of exits and entry Transmission depends on the source of the infectious agent, the portal of exist in the infectious host, and the portal of entry in the recipient host. The portals most commonly associated with human and animal diseases are: Respiratory: respiratory diseases, droplet and air-born transmission Genitourinary: sexually transmitted diseases Alimentary: portal of exit may be the mouth, exit – enteric diseases, feacal-oral transmission, food- and water-borne diseases Skin Superficial lesions: produce infectious discharges Percutaneous: occurs through mosquito bites or needles Transplacental: portal of exit from mother to fetus 01/15/2025 Mode of transmission The two basic modes are direct and indirect. Direct transmission occurs more or less immediately: contact with reservoir and droplet transmission Indirect transmission may occur through animate or inanimate mechanisms. Animate mechanisms involve vectors. Inanimate mechanisms: disease agents are spread by environmental vehicles or by air. Anything may be a vehicle, including objects, food, water, milk, or biological products or surgical instruments 01/15/2025 Susceptible host Susceptibility is affected by: Genetic factors: not yet well understood but seem to play role General resistance factors: many body functions that prevent infectious agent to enter the body Specific acquired immunity: Natural immunity and Artificial immunity (vaccination) Artificial: active and passive immunity 01/15/2025 Epidemic development Source: Introduction to Infectious disease epidemiology. 01/15/2025 Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Natural History Fraser et al PNAS 2004 Incubation period: Time from infection to symptoms onset Latent period: Time from infection to infectiousness onset Infectious period: Time during which the infected person is infectiousness Symptoms are readily observable or recallable The time of infection is most often not directly observable, but might be inferred from exposure history Diseases with higher pre-symptomatic infectiousness are generally more difficult to control (with symptoms-based interventions, e.g. isolation and contact tracing) “Factors that make an infectious disease outbreak controllable” Source: Introduction to Infectious disease epidemiology. 01/15/2025 Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Incubation period SARS-CoV-2: Xin et al Clin Infect Dis. 2021 SARS: Leung et al Ann Intern Med 2004 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 H7N9: Cowling et al Lancet 2004 Incubation period The incubation period can vary substantially among individuals: Route and dose of transmission Host genetics, age, immunity Intervention (e.g. pharmacologic prophylaxis and treatment) Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Viriogeux et al Emerge Infect Dis 2016 01/15/2025 Incubation period The incubation period can vary Younger patients have longer incubation substantially among individuals: period for AIDS Route and dose of transmission Host genetics, age, immunity Intervention (e.g. pharmacologic prophylaxis and treatment) Darby et al Lancet 1996 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Incubation period The incubation period can vary substantially Antiretroviral therapies lengthen the among individuals: incubation period of AIDS Route and dose of transmission Host genetics, age, immunity Intervention (e.g. pharmacologic prophylaxis and treatment) Darby et al Lancet 1996 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Incubation period distribution Typically, distribution is right-skewed, i.e. has a long right tail Often looks like a lognormal distribution (the log of incubation period is normally distributed) Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Incubation period: acute respiratory viral infections 4.0 SARS 3.1 Avian flu H7N9 3.3 Avian flu H5N1 1.4 Seasonal flu A 0.6 Seasonal flu B 12.5 Measles Incubation period (days) Lessler et al Lancet Inf Dis 2009 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Why do we want to know about incubation period? For clinical management: – To predict disease severity, e.g. shorter incubation time is associated with more severe outcome Risk of progression to death after AIDS diagnosis was reduced after widespread use of hyperactive antiretroviral therapies (HAART) 65 tetanus ICU cases 1961-1977, Leeds, UK Edmondson et al Survey of Anesthesiology 1980 Wong et al CID 2004 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025  Why do we want to know about incubation period? For public health control: To identify the origin of common-source outbreaks An epidemic of hepatitis A in Pennsylvania in 20 03 01/15/2025 Why do we want to know about incubation period? For public health control: – To estimate the duration necessary for quarantining suspected or contacts of cases to ensure that they are not infected upon release – Quarantine means isolating suspected cases and contacts from the community to prevent disease transmission in case they have been infected but do not yet have the clinical or virologic evidence of so. Set  high enough so that upon released from quarantine, the individual is uninfected with high probability, e.g.  = 95 or 99 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025  Clinical iceberg Morbidity and mortality observed in the model clinical settings often constitute only a small proportion of all infections in the population Death Asymptomatic or subclinical Hospitaliztion Medically attended Observed infection carriers are common for many infectious diseases H5N1 avian flu Almost 100% symptomatic Unobserved by healthcare system All Infections Polio infection Approximately 95% of persons infected with polio will have no symptoms. About 4 8% of infected persons have minor symptoms, such as fever, fatigue, nausea, headache, flu like symptoms, stiffness in the neck and back, and pain in the limbs, which often resolve completely. Fewer than 1% of polio cases result in permanent paralysis of the limbs (usually the legs). Of those paralyzed, 5 10% die when the paralysis strikes the respiratory muscles. The death rate increases with increasing age. 01/15/2025 US CDC Measures for transmissibility Infection attack rate – The proportion of a population (subgroup) infected over the course of an epidemic Secondary (infection) attack rate – The proportion of individuals infected in a semi-closed setting (e.g. households, airplanes, military barracks) in an outbreak caused by an index case (ideally accounting for pre-existing immunity) Basic reproductive number – The average number of secondary cases generated by an index case when an epidemic begins in a completely susceptible population Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Disease transmission Index case – the first case identified Primary case – the case bringing infection to a population Susceptible P Immune Clinical Sub-clinical Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Disease transmission Index case – the first case identified Primary case – the case bringing infection to a population Secondary case – infected by a primary case S Susceptible P S Immune Clinical S Sub-clinical Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Disease transmission Index case – the first case identified Primary case – the case bringing infection to a population Secondary case – infected by a primary case Tertiary case – infected by a secondary case T S Susceptible P S Immune Clinical S T Sub-clinical Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Secondary attack rate The secondary attack rate (SAR) is a measure used in epidemiology to assess the infectiousness of a disease. It represents the proportion of susceptible individuals who become infected after exposure to a primary case within a specific group, Susceptible such as a household or other close-contact setting. Immune SAR provides insight into how effectively a disease spreads in close- contact environments. Clinical 𝑛𝑜. 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠 Sub-clinical 𝑆𝐴𝑅 = 𝑛𝑜. 𝑜𝑓 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 (𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝑠) T S Components: P S 1.New cases among contacts: The number of secondary infections caused by a primary (index) case. 2.Total susceptible contacts: The total number of people exposed to the primary case who were not already S T immune (e.g., due to vaccination or previous infection). 01/15/2025 SAR: interpretation and application Interpretation: A higher SAR indicates that the disease spreads easily in close-contact settings, suggesting high transmissibility. A lower SAR suggests that the disease may be less contagious or that interventions (e.g., masking, isolation, or vaccination) are effective in reducing transmission. Applications: Estimating the potential impact of infectious diseases. Comparing the transmissibility of different diseases (e.g., influenza vs. COVID-19). Assessing the effectiveness of public health interventions in reducing transmission. 01/15/2025 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease SAR: exercise 1 In a workplace setting, an individual develops symptoms of an infectious disease and is confirmed as the primary case. The workplace has 20 employees in close contact with the infected person. Among these employees: 15 are susceptible 5 have immunity due to vaccination Over the next week, 6 of the susceptible employees develop the disease. Questions: 1.Calculate SAR in this workplace. 2.If another intervention reduces the new cases among contacts to 3, what would be the new SAR? 𝑛𝑜. 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠 𝑆𝐴𝑅 = 𝑛𝑜. 𝑜𝑓 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 (𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝑠) 01/15/2025 SAR: exercise 2 Two households are exposed to different index cases of the same disease: Household A: 5 susceptible members, 3 develop the disease. Household B: 10 susceptible members, 2 develop the disease. Questions: 1.Calculate the SAR for each household. 2.Compare the SARs and explain which household experienced higher transmission and why that might be the case. 01/15/2025 SAR: Exercise 3 A school outbreak involves 50 students exposed to a primary case during a class event. Among these: 40 students are susceptible. 16 students become infected. Questions: 1.Calculate the secondary attack rate (SAR). 2.If 5 additional students become infected but remain asymptomatic, does this change the SAR? Why or why not? 01/15/2025 Basic concepts for describing transmission Basic reproductive number, R0 The average number of secondary cases generated by an index case when an epidemic begins in a completely susceptible population. Mean generation time, Tg The average time it takes an index case to infect other individuals after he becomes infected. Epidemic growth rate, r The rate at which the number of infections is increasing exponentially During the early phase, the epidemic doubling time is t d = ln(2)/ r. Why? During this phase, the epidemic size is growing exponentially at rate r. Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Basic reproductive number, R0 The average number of secondary cases generated by an index case in a fully susceptible population: – Reproductive number, R: Same as R0 except that the population needs not be completely susceptible Some time after the epidemic has started, in which case we denote the reproductive number by Rt. If the population is partially vaccinated before the outbreak B A 2 +2 +3 R0 = =  3 C 1 st generation 2 nd generation Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 3 rd generation 01/15/2025 R0 interpretation R0​1: Each infected person causes more than one new infection. The disease can spread exponentially, leading to an epidemic. 01/15/2025 Basic reproductive number, R0 The average number of secondary cases generated by an index case in a fully susceptible population. R0 < 1: The epidemic will die out R0 > 1: The pathogen can lead to an without exponential growth exponentially growing epidemic Exponential growth 10 infected The epidemic dies out 10 infected seeds without exponential growth seeds How to estimate R0? Source: Introduction to Infectious disease epidemiology. Contract tracing and cohort follow-up. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Fitting mathematical models to epidemic curves. 01/15/2025 R0 estimation The exact formula for R0​ depends on the specific disease and its transmission dynamics. A general way to express R0​ is Where: β: Transmission rate (rate of contact between susceptible and infectious individuals and transmission probability). γ: Recovery rate (rate at which infected individuals recover or are removed from the population, i.e., 1/infectious period). Where: c: Average number of contacts per person per time. p: Probability of transmission per contact. d: Duration of infectiousness. 01/15/2025 SAR and R0 01/15/2025  Timescale of disease transmission Reproductive number describes the number of secondary cases but not how long it takes for infections to occur. Generation time: Time between successive infections. Serial interval: Time between symptom onset of successive infections. Source: Introduction to Infectious disease epidemiology. 01/15/2025 Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Serial interval and generation time 01/15/2025 Timescale of disease transmission Shorter generation time or serial interval means that confirmed and probable cases would need to be identified and removed from the population sooner in order to prevent them from spreading the disease. SARS Serial interval = 8 days 2nd infectee 3rd infectee 1st infectee Infections are prevented if isolated during this period Time since infection Influenza Serial interval = 3 days 2nd infectee 3rd infectee 1stinfectee Infections are prevented if isolated during this period Time since infection 01/15/2025 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Timescale of disease transmission Latent period The time it takes to become infectious after infection. Can be longer or shorter than incubation period. Isolation upon symptoms onset is VERYeffective for preventing transmission e.g. SARS Isolation upon symptoms onset is NOT effective for preventing transmission e.g. SARS-CoV-2 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025  Generation time = 5 days Generation time = 2 days Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease  Generation time = 5 days Generation time = 2 days Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease  Generation time = 5 days Generation time = 2 days Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease  Generation time = 5 days Generation time = 2 days Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Generation time = 5 days Generation time = 2 days Generation time = 5 days Generation time = 2 days Generation time = 5 days Generation time = 2 days Epidemic growth rate depends on R0 and Tg Mean generation time Tg: the average time it takes an index case to infect other individuals after he becomes infected. t1 t2 Tg = the average of t1, t2, t3, t 4 t3 t4 R0, Tg and epidemic growth rate r are interrelated. For a given R0, a shorter Tg means a higher growth rate. 𝑅0 = 1 + 𝑟𝑇𝑔 Source: Introduction to Infectious disease epidemiology. 𝑟 = (𝑅0 - 1 )/ 𝑇𝑔 Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Examples Imagine a disease with two different scenarios: 1.Scenario 1: 1. R0=3 2. Generation time: 3 days 3.Growth rate r: Faster, as the disease is spreading rapidly and cases are generated in a shorter time. 2.Scenario 2: 1. R0=2 2. Generation time: 7 days 3.Growth rate r: Slower, even though the reproductive number is still above 1, because the disease takes longer to spread between individuals. In both cases, the disease will spread exponentially, but the speed of spread (epidemic growth rate) will differ due to the generation time. 01/15/2025 Basic reproductive number and mean serial intervals of some pathogens Disease R0 Mean serial interval (days) Pandemic influenza 1.5 – 3 2.5 SARS 2–3 8 Measles 12 – 19 12 Smallpox 4–7 15 Chickenpox 4–9 14 Heffernan et al Royal Society Interface 2005 Fine Am J Epidemiol 2003 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Basic reproductive number of variant of SARS-COV-2 Du Clinic infect dis. 2022 Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 Exercises Basic Reproductive Number (R0​) Calculation In a study of a new infectious disease, it is observed that one infected individual causes an average of 4 new infections in a fully susceptible population. Questions: 1.What is the basic reproductive number (R0) of the disease? 2.If the R0 value is less than 1 in a population, what will happen to the epidemic? 01/15/2025 Exercises The basic reproductive number (R0) of a disease is 2.5, and the average generation time is 4 days. Questions: 1.Calculate the epidemic growth rate (r) using the formula: r=(R0−1)/Tg 2.If the generation time increases to 6 days, how would the epidemic growth rate change? 01/15/2025 Exercises Assume the R0 of a new disease is 3, and the generation time is 5 days. You are tasked with predicting the speed of an epidemic in a population where no one has immunity. Questions: 1.How fast will the disease spread in the population? (Use the relationship between R0 and generation time). r=(R0−1)/Tg 2. What can you infer if the generation time is reduced by half (i.e., to 2.5 days)? How would this change the epidemic dynamics? 01/15/2025 Exercises For a disease with a serial interval of 4 days, you are trying to reduce transmission through contact tracing and isolation. Questions: 1.If isolation is effective at reducing the average serial interval by 2 days (i.e., reducing it to 2 days), how would this affect the speed of the epidemic spread? 01/15/2025 Infectious disease modeling A systematic way of translating assumptions and data regarding disease transmission into quantitative description of how an epidemic evolves. Just like animal models, infectious disease modeling is a tool for helping you collect your thoughts about a complex problem to generate and test hypotheses. Some uses of infectious disease modeling: – Estimating transmission parameters from epidemiologic data – Estimating effectiveness of interventions from epidemiologic data, e.g. vaccination or school closure – Predicting the cost and effectiveness of intervention strategies, e.g. vaccinating core transmission group vs high-risk group Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025 The simplest epidemic model A closed population of size N is partitioned into three compartments of individuals: “Susceptible”, “Infectious”, and “Recovered” (SIR model). All individuals are assumed to be identical in terms of their (i) susceptibility to infection, (ii) Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Source: Introduction to Infectious disease epidemiology. infectiousness if infected, and (iii) mixing behavior associated with disease transmission (the so-called homogenous mixing assumption). Hallmarks of an epidemic: 1. The number of infections increases exponentially during the early phase of a growing epidemic 2. The epidemic curve is unimodal and peaks when the susceptible pool has been sufficiently depleted (such that Rt < 1) 2 Epidemiologic parameters: R0 = β/α, Tg = 1/α 1 r = (R0 −1)/Tg = β − α Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease SIR epidemic dynamics  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease SIR epidemic dynamics Exponential growth  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Depletion of susceptibles Attack rate increases Rdecreases SIR epidemic dynamics Exponential growth 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease The epidemic peaks Depletion of susceptibles Attack rate increases Rdrops to 1 SIR epidemic dynamics 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Incidence begins to drop Rdrops below 1 Depletion of susceptibles Attack rate increases SIR epidemic dynamics 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Rdrops below 1 Incidence drops monotonically Depletion of susceptibles Attack rate increases SIR epidemic dynamics 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease The epidemic Rdrops below 1 dies out Depletion of susceptibles Attack rate increases SIR epidemic dynamics 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease The epidemic Rdrops below 1 dies out Depletion of susceptibles Final attack rate SIR epidemic dynamics 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease The epidemic Final attack rate < 100% Rdrops below 1 dies out Depletion of susceptibles SIR epidemic dynamics 01/15/2025 Vaccination Suppose the vaccine is 100% efficacious. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Source: Introduction to Infectious disease epidemiology. It is not necessary to vaccinate the whole population to halt a growing epidemic. Why? – Vaccinating an individual indirectly reduces the risk of infection of this individual’s contacts (herd immunity). Infected Susceptible Vaccinated Vaccination with coverage p R = R0 R = R0(1−p) 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Vaccinated(100% directly protected) Susceptible Infected Herd immunity I 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Vaccinated(100% directly protected) Susceptible Infected I Herd immunity 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease I Vaccinated(100% directly protected) Susceptible Infected I Herd immunity 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease I Vaccinated(100% directly protected) Susceptible Infected I Herd immunity 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease I Vaccinated(100% directly protected) Susceptible Infected I Herd immunity 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Indirectly protected I Vaccinated(100% directly protected) Susceptible Infected I Herd immunity 01/15/2025 Herd Immunity The top box shows an outbreak in a community in which a few people are infected (shown in red) and the rest are healthy but unimmunized (shown in blue); the illness spreads freely through the population. The middle box shows a population where a small number have been immunized (shown in yellow); those not immunized become infected while those immunized do not. In the bottom box, a large proportion of the population have been immunized; this prevents the illness from spreading significantly, including to unimmunized people. In the first two examples, most healthy unimmunized people become infected, whereas in the bottom example only one fourth of the healthy unimmunized people become infected. https://en.wikipedia.org/wiki/Herd_immunity 01/15/2025 Critical vaccination coverage Suppose the vaccine is 100% efficacious. Critical vaccination coverage, c* – The minimal proportion needed to be vaccinated in order to Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Source: Introduction to Infectious disease epidemiology. prevent an epidemic. – Also called the herd immunity threshold In the SIR model, c* = 1–1/ R 0 , i.e. vaccinating a proportion p > 1–1/ R 0 of the population is sufficient to prevent an epidemic. Why? – After vaccination, the reproductive number is R = (1− p)R0 1  p 1 −1/ R0 01/15/2025 Herd immunity and vaccination coverage 01/15/2025 https://www.nature.com/articles/s41577-020-00479-7  Building more complexities into the model Stochasticity (“chance effects”) More detailed natural history , e.g. asymptomatic infections Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Source: Introduction to Infectious disease epidemiology. Age structure and multiple populations Aging, birth, deaths, immigration, emigration Seasonality and other time-dependent forcing Individual-based model instead of compartmental model 01/15/2025  Source: Introduction to Infectious disease epidemiology. Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease 15 SIR model with vaccination 01/15/2025 SIR with vaccination and mortality 01/15/2025 More detailed natural history Latent period – the period of time during which the infected individual is not yet infectious (e.g. the latent Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Source: Introduction to Infectious disease epidemiology. period is 14 days on average for smallpox) – 4 compartments: “Susceptible”, “Exposed”, “Infectious”, and “Recovered” S E I R More than one possible pathway, e.g. an infected individual develops symptoms only with probability p p I S E R 1− p A 01/15/2025 Age structure Age-specific transmissibility and natural history. βij: transmission rate from age group j to age group i. If Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Source: Introduction to Infectious disease epidemiology. there are n age groups, then there are n2 βij’s. 01/15/2025 Multiple populations While the assumption of homogenous mixing may be reasonable for within-population epidemic dynamics, it is obviously not valid when considering epidemic dynamics among different populations that Dr Tim K. Tsang. WHO Collaborating Centre for Infectious Disease Source: Introduction to Infectious disease epidemiology. are weakly interacting (e.g. Hong Kong and Beijing) Common models to simulate epidemic dynamics among populations (linked by human travel): meta- population models, gravity model 01/15/2025  Exercise in R 01/15/2025 THANK YOU! Questions? www.hei-planet.com