Modeling the interactions between pathogens, their hosts and their environment Arie Havelaar, Katsuhisa Takumi, Peter Teunis, Rob de Jonge and Johan

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1 Modeling the interactions between pathogens, their hosts and their environment Arie Havelaar, Katsuhisa Takumi, Peter Teunis, Rob de Jonge and Johan Garssen National Institute for Public Health and the Environment, Bilthoven, the Netherlands

2 Contents Background Hit theory models and the underlying assumptions Sources of data for dose-response modeling Volunteer experiments Outbreak investigations In vitro models In vivo and in silico models Future perspectives 2

3 WHO/FAO Guidelines on Hazard Characterization for Pathogens in Food and Water Initiated in a Workshop in Bilthoven, June 2000 Reviewed in expert meetings, public and peer review Final draft available July

4 The infectious disease process MATRIX Exposure DISEASE R Infection Acute illness PATHOGEN HOST Sequelae Mortality 4

5 Conceptual basis for dose response models Single hit Each inoculated organism has a (possibly very small but non zero) probability of infection and ilness, no matter how low the dose Each surviving organism grows to produce a clone of cells Independent action The mean probability per inoculated pathogen to cause a (symptomatic or fatal) infection is independent of their number Micro-organisms behave as discrete particles (Random distribution) Infection The organism is able to establish itself in the host and to actively multiply in the host tissues Detection usually by faecal excretion or seroconversion 5

6 Threshold or no threshold? Experimental exposure of Cynomolgus monkeys to natural aerosols from a goat hair processing plants; deaths due to Bacillus anthracis Brachman et al., Bact Rev 1966;30:

7 Hit-theory models (1) Assume a randomly mixed inoculum with mean dose D Individual doses are Poisson distributed Each inoculated organism encounters a number of barriers The probability of one organism surviving all barriers is p m Then, the probability that at least one organism survives all barriers follows the exponential relation Pr ( D; p m ) = e inf 1 D. p m 7

8 Hit-theory models (2) Different assumptions for p m lead to different functional forms of the dose-response model p m is constant: exponential model Pinf ( D; r) = 1 e D. r p m follows a Beta distribution: hypergeometric model P inf ( 1 1 D; α, β ) = 1 F ( α, α + β, D) Approximation: Beta-Poisson model P inf D ( D; α, β ) = 1 (1 + ) β α All models are approximately linear at low doses 8

9 Volunteer experiments Strengths direct observations in humans conditions of exposure controlled selection of pathogens, hosts and matrix possible Limitations ethical and economical healthy adults, no severe outcomes, small dose groups self-selection of volunteers laboratory adapted strains extensive purification and safety testing of inoculum 9

10 Campylobacter jejuni, volunteer experiment Hypergeometric model 10

11 Outbreak studies Outbreaks are natural, non-controlled experiments Strengths diverse host responses, including subgroups at risk may provide detailed insight in factors controlling exposure and illness risk of sequelae and mortality Limitations focus of investigation is to stop exposure case definitions chosen for efficiency no or inaccurate dose information incomplete case finding or unknown size of population at risk are outbreak strains representative of endemic strains? 11

12 An STEC O157 outbreak in Japan School lunch (salad, seafood sauce), Morioka City, Japan Well-defined population at risk Fecal samples from all exposed persons Samples of incriminated meal were available and analysed by quantitative methods (Shinagawa, 1997) Exposed Faecal positives Average ingested dose Children cfu person -1 Teachers cfu person -1 12

13 Dose-response models for Japanese outbreak (children) Exponential model Hypergeometric model 13

14 Comparison of DR models for STEC O157 Model Species Host organism Prob. illness per Reference single cell Exponential STEC O157 Children 9 x 10-3 Nauta et al Hypergeometric STEC O157 Children 6 x 10-3 Nauta et al Beta-Poisson S. dysenteriae, S. flexneri Adults 1 x 10-3 Cassin et al., 1998 Exponential STEC O157 Rabbit 6 x 10-8 Haas et al., 2000 Beta-Poisson (envelope) S. dysenteriae, EPEC Adults 5 x 10-5 Powell et al.,

15 In vivo experiments Oral exposure of rats to Salmonella Enteritidis Overnight fasting and suspension of inoculum in sodium bicarbonate Infection and inflammation of the intestinal tract and systemic infection No clinical illness except at very high doses 15

16 Dose-response model for colonization of spleen Spleen data Spleen exp. model P inf Log 10 dose (cfu) Exponential model: r = 1.2 x 10-3 (success in 1 per 800 infected cells) 16

17 Genetic background affects outcome Probability of infection per SE cell Lewis: 1 : 25,000 Wistar: 1: 800 Brown Norway 1:

18 Dose response model for continuous outcomes White blood cells (neutrophils, monocytes) are affected by oral infection with SE Decrease on day 0-3 (migration into tissue) followed by increase on day 4-6 (increased production by bone marrow) and gradual regression to background levels Neutrophils (cells/µl) Expt. 2, before Expt. 2, after Expt. 4, before Expt. 4,after Expt. 5, before Expt. 5, after Log 10 dose (cfu) 18

19 Continuous dose response model (1) The magnitude of the host response initially increases with dose, but eventually saturates to a maximum level Baseline response follows lognormal distribution Y If exactly one pathogen survives, there is a proportional increase in response The proportional increase varies between animals by a lognormal distribution Z Distribution of responses for animals infected by exactly 1,2,3, bacteria is YZ, YZ 2, YZ 3,.. 19

20 Continuous dose response model (2) Distribution of responses for animals inoculated with average dose 1/r,2/r,3/r, bacteria is YZ, YZ 2,YZ 3,.. The response saturates when the dose is equal to c/r c is the average number of bacteria independently initiating the infection when the response saturates to the maximun level 20

21 Continuous dose response model (3) P inf inf =1 e rd rd c tanh c X = P YZ + (1 P Y = lognormal(µ, ν) Z = lognormal(ρ,σ) inf )Y D: average dose r: probability of infection per SE cell Y: baseline neutrophil count; Z: proportional increase by multiplication of single SE cell c: number of surviving SE that initiate a saturating response 21

22 Neutrophil response on day 5 after infection Lewis rats Brown Norway rats c varies between 1 and 6 surviving cells 22

23 Comparison of different end-points Rat species Spleen DTH Neutrophils colonization Lewis 1:25,000-1:33,000 Wistar 1:800 1:130 1:3,000 Brown Norway 1:200-1:500 23

24 How to extrapolate from animals to humans? Direct: the dose-response model for man is the same as for the animal (possibly using safety factors ) Animal: r = 1 : 800 Extrapolated humans: r = 1 : 800 (or 80 or 8) Scale factors: the relative change between different (exposure or host) conditions is the same in animals and man Human (watery suspension): r = 1 : 1000 Animal (watery suspension): r = 1 : 5000 Animal (fatty food) r = 1 : 500 Extrapolated human (fatty food) r = 1 :

25 How to extrapolate from animals to humans? Paralellogram approach: the response in animals is modulated by the result of some in vitro test Animal: r = 1 : 800 Survival in animal stomach: 100% Survival in human stomach: 20% Extrapolated humans: r = 1 : 4000 Dynamic models: the relative change in parameter values is thesameinanimalsand man 25

26 In vitro and in silico models: passage of Escherichia coli through the stomach Predicted average gastric passage of E. coli strain 30 in a solid meal young: 47-73% elderly: 59-78% 26

27 But bacteria have many unknown secrets.. 1.0E+06 Viable count (cfu/ml) 1.0E E E E E+01 t = 0 min t = 30 min t = 60 min 1.0E+00 control 2 minutes 15 minutes 30 minutes Time of exposure to stomach ph 27

28 Dynamic models: the ultimate goal? Wigginton and Kirschner, Immune regulation during infection with M. tuberculosis, J Immunol 2001;166:

29 Conclusions The conceptual basis and mathematical methods for doseresponse models are well established The available data on effects of human exposure are and will be limited Outbreaks of water- and foodborne illness offer perspectives for additional human data Additional data sources must be developed: in vivo and in vitro models To extrapolate from these models to humans, sophisticated mathematical models are necessary 29