Eco-Epidemiology: Approach, Theory, and Models

1. Eco-Epidemiology: Approach, Theory, and Models

2. Densities of human populations, the character and quality of available water supply, food, and shelter together with the frequency and range of contacts among individuals...affect disease patterns significantly… …Great cities were, until recently, always unhealthy… …all such local disturbances of ecological relations have worked within a biological gradient characterized by an increase in the variety and frequency of infections as temperature and moisture increased. [William H. McNeil, Plagues and People (1976), page 51]

3. Dengue SE Asia

4. Japanese encephalitis in India

5. Nipah virus in Malaysia

6. Hanta virus In Southwest US

7. Dengue in the Americas

8. Dengue Americas

9. D = P E H Infectious Disease Emergence = Population growth x Environmental Change x Hygiene

10. D = P E H • Geographic expansion • Increased epidemic activity • New pathogen • New presentation • Antimicrobial resistance Infectious Disease Emergence = Population growth x Environmental Change x Hygiene

11. D = P E H Infectious Disease Emergence = Population growth x Environmental Change x Hygiene • Increased density • Increased dispersion • Increased mobility

12. D = P E H Infectious Disease Emergence = Population growth x Environmental Change x Hygiene • Regional Environmental Change • Global Climate Change

13. D = P E H Infectious Disease Emergence = Population growth x Environmental Change x Hygiene Public Health Infrastructure

14. D = P E H Infectious Disease Emergence = Population growth x Environmental Change x Hygiene • Increased density • Increased dispersion • Increased mobility

15. D = P E H Infectious Disease Emergence = Population growth x Environmental Change x Hygiene • Regional Environmental Change • Global Climate Change

16. D = P E H Infectious Disease Emergence = Population growth x Environmental Change x Hygiene Public Health Infrastructure

17. What are the environmental influences on disease? Infectious disease ecology attempts to address this question by: • Focusing on zoonotic and vector borne diseases; ~80% of EIDs especially if diseases that persist in the environment are included (e.g., polio virus, MRSA) • Considering ‘intrinsic’ (host-pathogen life history) and ‘extrinsic’ (environmental) factors – (biotic vs abiotic) • Attempting to elucidate and develop predictive models of disease emergence (as a basis for control and prevention) • Using a theoretical/analytical approach draws on ‘host-parasite biology’, functionally describes viral, bacterial, and protozoan pathogens as ‘microparasites’. Note: ‘infection’ in disease ecology ~ innoculation of a host not necessarily accompanied by a clinically detectable immune response.

18. D = P E H Infectious Disease Emergence = Population growth x Environmental Change x Hygiene

19. D = P E H • Geographic expansion • Increased epidemic activity • New pathogen • New presentation • Antimicrobial resistance Infectious Disease Emergence = Population growth x Environmental Change x Hygiene

20. What are the environmental influences on disease? Infectious disease ecology attempts to address this question by: • Focusing on zoonotic and vector borne diseases; ~80% of EIDs especially if diseases that persist in the environment are included (e.g., polio virus, MRSA) • Considering ‘intrinsic’ (host-pathogen life history) and ‘extrinsic’ (environmental) factors – (biotic vs abiotic) • Attempting to elucidate and develop predictive models of disease emergence (as a basis for control and prevention) • Using a theoretical/analytical approach draws on ‘host-parasite biology’, functionally describes viral, bacterial, and protozoan pathogens as ‘microparasites’. Note: ‘infection’ in disease ecology ~ innoculation of a host not necessarily accompanied by a clinically detectable immune response.

21. Zoonotic and Vector Borne Disease Definitions Zoonotic diseases are diseases caused by infectious agents that can be transmitted between (or are shared by) animals and humans Vector-borne diseases are diseases in which the pathogenic microorganism is transmitted from an infected individual to another individual by an arthropod or other agent, sometimes with other animals serving as intermediary hosts. Intermediary hosts such as domesticated and/or wild animals often serve as a reservoir for the pathogen until susceptible human populations are exposed.

22. Direct versus Indirect Transmission Definitive Host Host T2 T1 T1 Intermediate Host* T1 T2 Transmission parameters for the flow of the pathogen from the Defintive Host to the Intermediate Host and from the Intermediate Host to the Definitive Host *may be a vector or other reservoir

23. Pathogen Growth in a Host Population and Epidemiological Dynamics The SIR “Compartmental Model” births infected Susceptibles (uninfected) Recovered (immune) deaths deaths deaths

24. Exercise: Pathogen Growth in a Host Population: Introduction to the SIR Model births infecteds Recovered (immune) susceptibles

25. R0, The Basic Reproductive Rate of a Disease This single most important parameter determining whether or not a disease can spread, cause and epidemic, and whether or not a disease will be epidemic or endemic - or become a pandemic! The quantity R0 determines expresses a combination factors including providing insights into: (1) How transmissable disease is (2) How controllable an epidemic will be (3) How the disease can be controlled

26. Determinants of R0 and Re For many microparasites with direct transmission R0 and Re (The “effective reproductive rate) increases with: The period of time over which an infected host remains infectious. When higher host densities offer more opportunities for transmission. The transmission rate of the disease, which depends both on the intrinsic infectiousness of the disease as well as on patterns of host behavior that increase the likelihood of infectious and susceptible hosts coming together.

27. I. Discrete, compartmental Model of R0 As in Begon et al. (where R0 is in theory in not a fixed “intrinsic rate” of growth, R0 is allowed to be like Re): • For microparasites with direct, density dependent transmission R0 can said to increase with: • the average period of time a host remains infectious, L • the number of susceptible individuals, S • the transmission coefficient, β • So, overall: • R0 = SβL

28. Expressing the Transmission Threshold A critical population size, St, can be expressed where R0 = 1 So, at that threshold: St = 1/(βL) • In populations with numbers of susceptibles less than this, the infection will die out (R0 < 1)

29. Consider the Different Kinds of Population • Microparasites are highly infectious (large βs) • Microparasites give rise to long periods of infection (large Ls) • ….produce high R0s • What kinds of parasite populations would behave like this? • Also, differences in the parameters β and L can determine whether a disease becomes endemic or not….. • What other factors or parameters (hint: mobility)

30. Epidemic Disease # of cases Time

31. Endemic Disease # of cases Time

32. II. Continuous Model (calculus!!) for Direct Transmission and the Basic Reproductive Rate of a Disease, R0

33. Explicit Definitions of R0 (as used by Anderson and May in continuous model derivations) R0, “the basic reproductive rate,” is the average number of successful offspring a microparasite is intrinsically capable of producing. More precisely, in the case of the compartmental model, R0 is average number of secondary infections when one infected individual is introduced into a population where everyone is susceptible. R0 is mainly a theoretical concept that is extremely important in mathematical ecological epidemiology for deriving numerous equations valuable in infectious disease research.

34. Re, The Effective Rate of Reproduction R0 is extremely difficult to measure for ecologists, so Re, the “effective reproductive rate of a disease” can be a more useful practical tool. The effective reproductive rate, Re, is the is equal the basic reproductive rate, R0, discounted by the fraction, x*, of the host population that is susceptible at equilibrium. x*can be estimated from serological data. At equilibrium, Re =1, therefore, R0x* = 1 The density-depend process of holding Re below R0 is simply the removal of susceptible individuals from the population by immunity. In reality, various factors intervene to prevent “runaway” exponential growth of an infection in a population besides the increasing density of immune individuals – microparasites are affected by all of the same kinds of abiotic and biotic regulatory factors as any population of organisms.

35. Considering Immunity Alone Considering Immunity alone, if a proportion p is becomes immune (by natural infection or a public health immunization program) the proportion remaining susceptible is at most x* =1 – p. Therefore, ReR0 (1-p) If the right hand side of the equation is less than 1, then Re < 1, and the infection will not be able to maintain itself in the host population.

36. Considering Immunity Alone* Thus, the critical proportion, pc of a population to be immunized (holding population density constant along with other assumptions like complete mixing) for eradication of a disease is: pc = 1 – (1/ R0) *For many diseases Immunity is by far the most important factor, outweighing all other factors together

37. Examples of Real pc Values from Anderson and May (1991) Immunization coverage in Africa of about 80% succeeded in eradicating the smallpox virus, but not in India where the lowest population densities (17/km2) where still greater than the highest densities in Africa (13/km2). “Re” was basically reduced toless than one by immunizing a smaller fraction of the population in Africa than in India.

38. Host Threshold Density - A key Concept in Eco-Epidemiology pc can be restated, as the concept was originally developed by Kermack and McKendrick (1927) as: Host Threshold Density (NT) – the population density below which Re< 1 for a given parasite, and an epidemic or epizootic, thus the establishment of a pathogen in a human or animal reservoir (including vector) host population, is not possible.

39. Model for the Basic Reproductive Rate (R0): Directly Transmitted Microparasite R0= e( S/Γ)-1 This is satisfactory in explaning/predicting the dynamic behavior of directly transmitted diseases independent of social behavior (like measles, pertussis, etc.)

40. Basic Reproductive Rate (R0): Directly Transmitted Microparasite R0= e( S/Γ)-1 density of susceptibles Satisfactory in explaning/predicting the dynamic behavior of directly transmitted diseases independent of social behavior (like measles, pertussis, etc.)

41. Basic Reproductive Rate (R0): Directly Transmitted Microparasite R0= e( S/Γ)-1 rate of depletion of infective pool though death or recovery density of susceptibles Satisfactory in explaning/predicting the dynamic behavior of directly transmitted diseases independent of social behavior (like measles, pertussis, etc.)

42. Basic Reproductive Rate (R0): Directly Transmitted Microparasite R0= e( S/Γ)-1 rate of depletion of infective pool though death or recovery density of susceptibles transmission coefficient Satisfactory in explaning/predicting the dynamic behavior of directly transmitted diseases independent of social behavior (like measles, pertussis, etc.)

43. Actual Number of measles cases reported in New-York, 1928-1971 Model Simulation Number of new cases of measles in a population of 1M individuals (birth rate equal to death rate = 0.0000351; R=15)

44. Generation =time 1 2 3 4 5 6 7 8 Rt 1 1 2 2/2 3/2 4/3 6/4 7/6 Chains of Transmission in SARS (discrete generation model from Anderson et al. 2005)

45. Chains of transmission between hosts Generation =time 1 2 3 4 5 6 7 8 Rt 1 1 2 2/2 3/2 4/3 6/4 7/6 Chains of Transmission in SARS(discrete generation model from Anderson et al. 2005) Effective reproductive number = number of new infections caused by each new case at time, t.

46. Indirect Transmission: The Case of Malaria

47. Generation =time 1 2 3 4 5 6 7 8 Chains of Transmission in a Malaria Rt 1 3/1 8/3 14/8 ………………

48. Generation =time 1 2 3 4 5 6 7 8 Chains of Transmission in a Malaria Rt 1 3/1 8/3 14/8 ……………… Mosquitos’ mobility effectively spatially homogenizes human population locally, resulting in an R0 approaching N2.

49. Generation =time 1 2 3 4 5 6 7 8 Chains of Transmission in a Malaria Rt 1 3/1 8/3 14/8 ……………… Mosquitos’ mobility effectively spatially homogenizes human population locally, resulting in an R0 approaching N2. R0 for malaria reported to be as high as 80, and even in 1000 locally!

50. Malaria Model Parameters Assume a single primary case with a recovery rate of y, where the average time spent in an infectious state is 1/y. During this time, the average number of mosquito bites received fromm susceptible mosquitoes, each with a biting rate a is am/y. Of these mosquitoes a proportion c is actually infectious, which gives a total of amc/y mosquitoes infected by the primary human case. Each of these mosquitoes survives for an average time of 1/, where  is the per capita mortality rate. Each makes a total of ab/ bites, where b is the proportion of infectious bites on humans that produces a patent infection. The total number of secondary cases is thus (ab/)(amc/y). Note that a enters into the equation twice since the mosquito biting rate controls transmission from humans to mosquitoes and mosquitoes to humans.