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Modeling antibiotic resistance in populations: from deterministic to stochastic to

agent-based models.

Laura TEMIME

G Thomas, PY Boëlle, D GuillemotL Opatowski, Y Pannet

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Modeling antibiotic resistance in populations

Why model resistance? To achieve better understanding of underlying

processes in resistance selection To predict future changes To evaluate control measures such as:

– Reduction of antibiotic consumption in the community– Hand washing, systematic isolation or use of rapid

diagnostic tests in hospitals

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Different modeling approaches

Available approaches for modeling antibiotic resistance selection in a population:

In large communities (e.g. country):– Compartmental deterministic models

Good prediction of the average behavior In smaller settings (e.g. schools, hospitals):

– Compartmental stochastic models Information on the variability of processes

– Agent-based models Data on the individual level

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Presentation outline

Modeling pneumococcal resistance to penicillin using a compartmental model:

– Deterministic model– Stochastic model

Several papers between 2003 and 2006 Modeling the selection and spread of antibiotic

resistance in hospital settings:– Individual-based model

Preliminary results, work in progress

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I- Modeling the selection of pneumococcal resistance to penicillin

in France

A deterministic model

(Temime L, Boëlle PY, Courvalin P, Guillemot D; Emerg Infect Dis, 2003)

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Context overview

S. pneumoniae:– Human pathogen (otitis, pneumonia, meningitis)

3-5 million deaths / year worldwide– Frequent asymptomatic carriage

Up to 40% carriers among children– Widespread antibiotic resistance

In France over 60% of strains exhibit decreased sensitivity to penicillin

frequently observed multiple resistance

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A specific resistance mechanism

S. pneumoniae resistance to penicillin:

Progressive decrease of sensitivity (MIC)

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A specific model

Objective = combining two levels for pneumococcal resistance selection:

– Intra-individual evolution of strains

reproducing the resistance mechanism – Inter-individual transmission of strains

Model characteristics:– Compartmental deterministic model (partial differential equations)– Progressive increase of resistance levels

Colonized compartments structured by MIC (continuous)

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A specific model: illustration

Unexposed to antibiotics Exposed to antibiotics

Genetic events

progressive MIC increase

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Model parameters

Parameters which may be controlled

Frequency and duration of -lactam exposure

Parameters which are documented in the literature

Frequency and duration of pneumococcal colonization Resistance mechanism

Parameters which require calibration

Transmissibility of pneumococci in a population

8 days1 tmt / 2 yrs

2.2 months

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Effects of antibiotic exposure

Colonization may persist with probability:

MIC may increase due to genetic events, according to the law:

2

2

05.0 m

m

(m) =

0,.π

2.4

2.8 de d(d) =

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Validation of model predictions

Model predictions CNRP data (87-97)

• 1987 : mostly antibiotic sensitive strains• 1997 : bimodal distribution of MICs

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Applications of this deterministic model

Predictions for N. meningitidis:– Differences in resistance levels of pneumococci and

meningococci can be explained by their natural histories of colonization alone

– High resistance levels expected in years to come

Pneumococcal conjugate vaccination:– Short-term impact on carriage and resistance– BUT expected re-increase in resistance in the long-term,

due to replacement of vaccine strains by non-vaccine strains which will become resistant

(Temime L, Boëlle PY, Valleron AJ, Guillemot D; Epid Infect, 2005)(Temime L, Guillemot D, Boëlle PY; Antimicrob Agents Chemother, 2004)

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II- Modeling the selection of pneumococcal resistance to penicillin

A stochastic model

(Temime L, Boëlle PY, Courvalin P, Guillemot D; Emerg Infect Dis, 2003)(Temime L, Boëlle PY, Thomas G; Math Pop Studies, 2005)

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Motivation

Shortcomings of the deterministic model:– Averaged predictions– No information on variability– Identical predictions regardless of population size

Developing a stochastic version of the model will allow:

– More realism in the description– Better predictions in small populations– Information on the variability of predicted phenomena

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General principles

Same compartmental model than in the deterministic setting

But transitions between compartments are considered random

Associated transition probabilities

Unexposed to antibiotics Exposed to antibiotics

For large population sizes, the deterministic solution approximates the mean stochastic epidemics

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Results in a town-like community (1000 individuals)

Time before 20% of strains will have reached this MIC

For a given MIC:

Time before the first emergence of a strain with this MIC

Penicillin-resistant pneumococcal strains will emerge on average 20 years after the introduction of penicillin, but it may be 10-30 years.

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III- Modeling the selection of S. aureus multi-resistance in hospital settings

(ICUs)

An agent-based model

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Context overview

Staphylococcus aureus :– Human pathogen (skin infections, septicemia, endocarditis)– 10-40% asymptomatic carriers– Colonization duration??

Antibiotic resistance :– Widespread penicillin resistance– Methicillin resistance (MRSA) common in hospital settings

since the 1960’s (30-50% of all strains)– Emergence of MRSA in the community in recent years

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Some important questions

What are the determinants for persistence of a staphylococcal strain in a hospital setting?

Why aren’t NO-MRSA successful outside hospitals? Which context could allow for the successful

introduction of CA-MRSA in hospitals? What would be the consequences?

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Why an agent-based model?

Individual-based or agent-based modeling has proved useful for:

– Modeling epidemic spread in an urban network (Eubank et al., Nature, 2004) or even at a countrywide scale (Longini et al., Am J Epid, 2004)

– Simulating healthcare activities in a hospital setting (Boelle et al., Comput Biom Res, 1998)

– Modeling pathogen dissemination in an ICU (Hotchkiss et al., Crit Care Med, 2005) and interventions

Allows for more realism and easier description of individual behaviors

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Model structure: hospital ward (ICU)

Patient 1

Ward corridors / Staff room

Doctors Nurses1 2 3 4

Patient 2 Patient 3 Patient 4

1 2 3 4

…

… …

ROOMS…

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Model structure: agents and agent characteristics

Human Agent Characteristics Environment

Patient Length of stay

Healthcare burden

Colonized ?

→ Colonizing strain, site of colonization

Room

Healthcare worker Daily task-list

Hygiene compliance

Colonized ?

→ Colonizing strain, site of colonization

Affected patients

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Model structure: agents and agent characteristics (2)

Agent Characteristics Environment

Micro-organism Carriage duration

Transmissibility

Conferred immunity and cross-immunity

Colonized

human agents

Antimicrobial agent Mechanism of action

Efficacy on present micro-organisms

Exposed

human agents

Transmission of colonization through infectious contacts

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First model outcomes (1)

Real-time graphical display of the hospital ward:

Follow-up of the geographical spread of micro-organisms

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First model outcomes (2)

Temporal changes in proportions of colonized individuals:

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First model outcomes (3)

Who colonized whom? History of transmission:

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Perspectives for the ABM

Lots of possible uses:– Educational tool– Assessment of control measures taking into account

individual behaviors (non compliance)– Predictions for dominance in a two strain-environment

(CA-MRSA and NO-MRSA)

Disadvantages:– Not a mathematical model no analytical expression available– Costly in simulation time– Large amount of data needed

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Need for data:complex models require complex data

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Need for data

Data for model building (parameter values):– Micro-organism characteristics (duration of colonization,

invasivity, ...)– Human characteristics (daily activities and contacts,

immunity status, ...)– Resistance characteristics (mechanism of emergence,

current susceptibility levels, ...) Data for model validation:

– Historical data on emergence and spread of resistant strains in specific settings

Allows comparison with model predictions

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Specific needs for different kinds of models

The amount of required data increases with model complexity:

Compartmental models:– Mean characteristics in the population: duration and

frequency of antibiotic exposure, infectious contact rate– Mean characteristics of the micro-organism: duration of

colonization, susceptibility to antibiotic exposure– Resistance mechanism characteristics

Agent-based models:– Similar characteristics at the individual level– Supplemental data on individual behaviors

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Infectious contact rate

Complex parameter which includes:– The frequency of inter-human contacts– The transmissibility of the micro-organism

Estimation strategies:– Not directly observed in populations– Often calibrated to reflect observed colonization– May be estimated using MCMC methods from longitudinal

data (Cauchemez et al., BMC Inf Dis, 2006)– Will be measured in hospital settings using “contact tracers”

carried by staff and patients (MOSAR project, WP7)

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Conclusions and perspectives

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Conclusions

Rising impact of the modeling approach to study antibiotic resistance selection over the last 15 years :

– More published models– More cited by a wider audience

Recent developments: more complex models which require more complex data

Antibiotic resistance modeling can only be satisfyingly achieved through a collaboration with microbiologists, physicians, etc.