Rapid loss of immunity is necessary to explain historical cholera epidemics

Transcription

1 Rapid loss of immunity is necessary to explain historical cholera epidemics Ed Ionides & Aaron King University of Michigan Departments of Statistics and Ecology & Evolutionary Biology

2 Bengal: cholera s homeland

3 Bengal: cholera s homeland

4 Bengal: cholera s homeland

5 Bengal: cholera s homeland

6 Bengal: cholera s homeland

7 Cholera: unsolved puzzles Mode of transmission contaminated water: environmental reservoir food-borne/direct fecal-oral transient hyperinfectious state (<18 hr)

8 Cholera: unsolved puzzles Mode of transmission contaminated water: environmental reservoir food-borne/direct fecal-oral transient hyperinfectious state (<18 hr) Seasonality two peaks per year

9 Cholera: unsolved puzzles Dacca cholera mortality J F M A M J J A S O N D

10 Cholera: unsolved puzzles Mode of transmission contaminated water: environmental reservoir food-borne/direct fecal-oral transient hyperinfectious state (<18 hr) Seasonality two peaks per year regional climate drivers: monsoon rainfall and winter temperatures?

11 Cholera: unsolved puzzles Mode of transmission contaminated water: environmental reservoir food-borne/direct fecal-oral transient hyperinfectious state (<18 hr) Seasonality two peaks per year regional climate drivers: monsoon rainfall and winter temperatures? Multi-year climate drivers El Niño-Southern Oscillation (ENSO)

12 Cholera: unsolved puzzles Mode of transmission contaminated water: environmental reservoir food-borne/direct fecal-oral transient hyperinfectious state (<18 hr) Seasonality two peaks per year regional climate drivers: monsoon rainfall and winter temperatures? Multi-year climate drivers El Niño-Southern Oscillation (ENSO) Immunity volunteer studies: > 3 yr immunity following severe infection community study of reinfections in Matlab, Bangladesh: risk of reinfection equal to risk of primary infection 1.6 yr average duration between primary infection and reinfection retrospective statistical analyses (Koelle & Pascual 2004): 7 10 yr immunity following severe infection

13 Inapparent infections most cholera infections are mild or asymptomatic

14 Inapparent infections most cholera infections are mild or asymptomatic reports of the asymptomatic:symptomatic ratio range from 3 to 100

15 Inapparent infections most cholera infections are mild or asymptomatic reports of the asymptomatic:symptomatic ratio range from 3 to 100 it is easy to underestimate the degree to which one underestimates a quantity one cannot observe

16 Inapparent infections most cholera infections are mild or asymptomatic reports of the asymptomatic:symptomatic ratio range from 3 to 100 it is easy to underestimate the degree to which one underestimates a quantity one cannot observe Needed: an approach that allows indirect inference about unobserved variables

17 Inapparent infections most cholera infections are mild or asymptomatic reports of the asymptomatic:symptomatic ratio range from 3 to 100 it is easy to underestimate the degree to which one underestimates a quantity one cannot observe Needed: an approach that allows indirect inference about unobserved variables historical cholera mortality records are a rich source of information, but have been difficult to fully exploit

18 Historical cholera mortality Jaipaguri Dinajpur Rangpur Malda Bogra Rashahi Mymensingh Mohrshidabad Pabna Birbhum Dacca Nadia Bankura Burdwan Jessore Faridpur Tippera Hooghly Noakhali Midnapur HowrathCalcutta 24 Parganas Khulna Bakergang Chittagong

19 Historical cholera mortality Jaipaguri Dinajpur Rangpur Malda Bogra Rashahi Mymensingh Mohrshidabad Pabna Birbhum Dacca Nadia Bankura Burdwan Jessore Faridpur Tippera Hooghly Noakhali Midnapur HowrathCalcutta 24 Parganas Khulna Bakergang Chittagong

20 Historical cholera mortality Dacca cholera mortality year

21 Historical cholera mortality Jaipaguri Dinajpur Rangpur Malda Bogra Rashahi Mymensingh Mohrshidabad Pabna Birbhum Dacca Nadia Bankura Burdwan Jessore Faridpur Tippera Hooghly Noakhali Midnapur HowrathCalcutta 24 Parganas Khulna Bakergang Chittagong

22 Historical cholera mortality Midnapur cholera mortality year

23 Historical cholera mortality Jaipaguri Dinajpur Rangpur Malda Bogra Rashahi Mymensingh Mohrshidabad Pabna Birbhum Dacca Nadia Bankura Burdwan Jessore Faridpur Tippera Hooghly Noakhali Midnapur HowrathCalcutta 24 Parganas Khulna Bakergang Chittagong

24 Historical cholera mortality Jaipaguri cholera mortality year

25 Historical cholera mortality Jaipaguri Dinajpur Rangpur Malda Bogra Rashahi Mymensingh Mohrshidabad Pabna Birbhum Dacca Nadia Bankura Burdwan Jessore Faridpur Tippera Hooghly Noakhali Midnapur HowrathCalcutta 24 Parganas Khulna Bakergang Chittagong

26 Historical cholera mortality Bakergang cholera mortality year

27 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε parameter symbol force of infection λ(t) recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k

28 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε parameter symbol force of infection λ(t) recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k

29 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε parameter symbol force of infection λ(t) recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k

30 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε parameter symbol force of infection λ(t) recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k

31 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε parameter symbol force of infection λ(t) recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k

32 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε λ(t) = ( e β trend t β seas (t) + ξ(t) ) I(t) P(t) + ω

33 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε λ(t) = ( ) e β trend I(t) t β seas (t) + ξ(t) P(t) + ω β trend = trend in transmission

34 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε λ(t) = ( ) e β trend I(t) t β seas (t) + ξ(t) P(t) + ω β seas (t) = seasonality in transmission semimechanistic approach: use flexible function

35 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε λ(t) = ( ) e β trend I(t) t β seas (t) + ξ(t) P(t) + ω ξ(t) = environmental stochasticity

36 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε λ(t) = ( ) e β trend I(t) t β seas (t) + ξ(t) P(t) + ω ω = environmental reservoir

37 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε λ(t) = ( ) e β trend I(t) t β seas (t) + ξ(t) P(t) + ω P(t) = censused population size

38 SIRS model ds = dp(t) + δ P(t) (λ(t) + kɛ R k + δ) S dt dt di = λ(t) S (m + γ + δ) I(t) dt dr 1 = γ I (k ɛ + δ) R 1 dt. dr k dt = k ɛ R k 1 (k ɛ + δ) R k Stochastic force of infection: ( ) λ(t) = e β trend I(t) t β seas (t) + ξ(t) P(t) + ω

39 Likelihood maximization by iterated filtering new frequentist approach (Ionides, Bretó, & King, PNAS 2006) can accommodate: continuous-time models nonlinearity stochasticity unobserved variables measurement error nonstationarity covariates based on well-studied sequential Monte Carlo methods (particle filter) plug and play property Implemented in pomp, an open-source R package (

40 Duration of immunity profile log likelihood immune period (yr)

41 SIRS model m M P b λ(t) γ S I R kε 1... kε R k kε parameter symbol force of infection λ(t) recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k

42 SIRS model predictions estimated cholera fatality (across districts): ±

43 SIRS model predictions estimated cholera fatality (across districts): ± in the historical period, fatality in severe cases was c. 60%

44 SIRS model predictions estimated cholera fatality (across districts): ± in the historical period, fatality in severe cases was c. 60% model prediction: lots of silent shedders

45 SIRS model predictions estimated cholera fatality (across districts): ± in the historical period, fatality in severe cases was c. 60% model prediction: lots of silent shedders evidence for silent shedders is mixed and weak

46 SIRS model predictions estimated cholera fatality (across districts): ± in the historical period, fatality in severe cases was c. 60% model prediction: lots of silent shedders evidence for silent shedders is mixed and weak Q: is it necessary that all exposed individuals become infectious?

47 Two-path model m M cλ(t) I γ R 1 kε... kε R k P b S kε (1 c)λ(t) Y ρ parameter symbol force of infection λ(t) probability of severe infection c recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k mean short-term immune period 1/ρ

48 Two-path model m M cλ(t) I γ R 1 kε... kε R k P b S kε (1 c)λ(t) Y ρ parameter symbol force of infection λ(t) probability of severe infection c recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k mean short-term immune period 1/ρ

49 Two-path model m M cλ(t) I γ R 1 kε... kε R k P b S kε (1 c)λ(t) Y ρ parameter symbol force of infection λ(t) probability of severe infection c recovery rate γ disease death rate m mean long-term immune period 1/ε CV of long-term immune period 1/ k mean short-term immune period 1/ρ

50 Two-path model ds = kɛ R k + ρ Y + dp(t) + δ P(t) (λ(t) + δ) S dt dt di = c λ(t) S (m + γ + δ) I(t) dt dy = (1 c) λ(t) S (ρ + δ) Y dt dr 1 = γ I (k ɛ + δ) R 1 dt. dr k dt = k ɛ R k 1 (k ɛ + δ) R k Stochastic force of infection: ( ) λ(t) = e β trend I(t) t β seas (t) + ξ(t) P(t) + ω

51 Model comparison model log likelihood AIC two-path SIRS SARMA((2,2) (1,1)) Koelle & Pascual (2004) seasonal mean

52 Goodness of fit district r 2 district r 2 Bakergang Jessore Bankura Khulna Birbhum Malda Bogra Midnapur Burdwan Mohrshidabad Calcutta Mymensingh Chittagong Nadia Dacca Noakhali Dinajpur Pabna Faridpur Rangpur Hooghly Rashahi Howrath Tippera Jaipaguri Parganas 0.839

53 Goodness of fit r 2

54 Simulated vs. actual data actual Dacca actual Faridpur actual simulated Dacca simulated Faridpur simulated SIRS model

55 Simulated vs. actual data actual Dacca actual Faridpur actual simulated Dacca simulated Faridpur simulated two-path model

56 Parameter estimates cholera fatality: 0.07 ± 0.05

57 Parameter estimates cholera fatality: 0.07 ± 0.05 probability of severe infection: ĉ = ± 0.005

58 Parameter estimates cholera fatality: 0.07 ± 0.05 probability of severe infection: ĉ = ± ˆR0 = 1.10 ± 0.27

59 Parameter estimates R 0 (t) J F M A M J J A S O N D J

60 Parameter estimates cholera fatality: 0.07 ± 0.05 probability of severe infection: ĉ = ± ˆR0 = 1.10 ± 0.27

61 Parameter estimates cholera fatality: 0.07 ± 0.05 probability of severe infection: ĉ = ± ˆR0 = 1.10 ± 0.27 duration of long-term immunity: 2.6 ± 1.8 yr

62 Parameter estimates cholera fatality: 0.07 ± 0.05 probability of severe infection: ĉ = ± ˆR0 = 1.10 ± 0.27 duration of long-term immunity: 2.6 ± 1.8 yr duration of short-term immunity: wk

63 Parameter estimates cholera fatality: 0.07 ± 0.05 probability of severe infection: ĉ = ± ˆR0 = 1.10 ± 0.27 duration of long-term immunity: 2.6 ± 1.8 yr duration of short-term immunity: wk geographical variability in force of infection

64 Geographical patterns environmental reservoir ω

65 Geographical patterns transmission, Jan Feb b 0

66 Geographical patterns transmission, Mar Apr b 1

67 Geographical patterns transmission, May Jun b 2

68 Geographical patterns transmission, Jul Aug b 3

69 Geographical patterns transmission, Sep Oct b 4

70 Geographical patterns transmission, Nov Dec b 5

71 Contrasting views of endemic cholera dynamics View of Koelle & Pascual (2004): long-term immunity (7 10 yr) modest asymptomatic ratio (c. 70:1) spatial heterogeneity slows epidemic seasonal drop in transmission stops epidemic waning of immunity interacts with climate drivers on multi-year scale

72 Contrasting views of endemic cholera dynamics New view: rapidly waning immunity high asymptomatic ratio (>160:1) susceptible depletion slows and stops epidemic loss of immunity replenishes susceptibles rapidly waning of immunity interacts with climate drivers on seasonal scale multi-year climate drivers?

73 Public health implications What determines the switch probability c?

74 Public health implications What determines the switch probability c? serological profile data suggest c declines with age

75 Public health implications McCormack et al. (1969)

76 Public health implications What determines the switch probability c? serological profile data suggest c declines with age dose/hyperinfectiousness foodborne/direct fecal-oral mode is most important lower doses provide short-term immunity

77 Public health implications What determines the switch probability c? serological profile data suggest c declines with age dose/hyperinfectiousness foodborne/direct fecal-oral mode is most important lower doses provide short-term immunity unintended consequences of neglect of household transmission?

78 Public health implications What determines the switch probability c? serological profile data suggest c declines with age dose/hyperinfectiousness foodborne/direct fecal-oral mode is most important lower doses provide short-term immunity unintended consequences of neglect of household transmission? presence of vibriophage in environment?

79 Alternative hypotheses? inhomogeneities behavioral effects

80 Extensions Recent data ( , Matlab, Bangladesh) Discrete population continuous time models Other diseases malaria measles influenza

81 Seasonality R. G. Feachem (1982) on the seasonal patterns of cholera epidemics in Bengal: They are such a dominant feature of cholera epidemiology, and in such contrast to the other bacterial diarrhoeas which peak during the monsoon in mid-summer, that their explanation probably holds the key to fundamental insights into cholera transmission, ecology, and control.

82 Seasonality R. G. Feachem (1982) on the seasonal patterns of cholera epidemics in Bengal: They are such a dominant feature of cholera epidemiology, and in such contrast to the other bacterial diarrhoeas which peak during the monsoon in mid-summer, that their explanation probably holds the key to fundamental insights into cholera transmission, ecology, and control. to understand seasonality, we must allow for the interaction of short-term immunity with seasonal environmental drivers

83 Thanks to... Mercedes Pascual Menno Bouma Carles Bretó Katia Koelle Diego Ruiz Moreno Andy Dobson the R project ( NSF/NIH Ecology of Infectious Diseases

84 Thank you!