Download Modelling and Control Issues Arising from Antibiotic Resistant

Mathematical Modelling and
Challenges in the Development of Drug
Resistance
Mary Ann Horn
Joint work with Erika D’Agata, Harvard Medical
School and Glenn Webb, Vanderbilt University
Vanderbilt University
Department of Mathematics
Enterococci
What are enterococci?
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•
Enterococci are bacteria found
in the faeces of most humans
and many animals.
•
Two types of enterococci are
associated with normal healthy
people, Enterococcus faecalis
and Enterococcus faecium.
Photo credit: University of Oklahoma Health Sciences Center
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Enterococci
Issues
•
•
•
Associated with both community
and hospital-acquired infections
Among the vanguard of
antibiotic resistant bacteria
Have acquired resistance genes
to counter antibiotics that were
once effective
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Photo credit: University of Oklahoma Health Sciences Center
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Nosocomial Infections
What does “nosocomial” mean?
“Even a term adopted by the CDC--nosocomial infection
obscures the true source of the germs. Nosocomial,
derived from Latin, means hospital-acquired. CDC
records show that the term was used to shield hospitals
from the ‘embarrassment’ of germ-related deaths and
injuries.”
-- Michael J. Berens, Chicago Tribune, July 22, 2002
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What infections are caused by enterococci?
• Most common infections are urinary tract infections
and wound infections.
• Infections threatening severely ill patients include
infection of the bloodstream (bacteraemia), heart
valves (endocarditis) and the brain (meningitis).
• Enterococci frequently colonize open wounds and
skin ulcers.
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Antibiotic Resistance
• Most enterococci have inherent resistance to various drugs
–
–
–
–
Cephalosporins
Semi-synthetic penicillinase-resistant penicillins
Clindamycin
Aminoglycosides
• Relatively resistant to other drugs
– Penicillin
– Ampicillin
• Tolerant to cell-wall active agents
– Ampicillin
– Vancomycin
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Antibiotic Resistance (con’t)
• Developed resistance
– Plasmid-resistance
Definition: A plasmid is an extrachromosomal ring of DNA
(particularly of bacteria that replicate autonomously)
– Transposon-mediated resistance
• Tetracycline, minocycline, doxycycline
• Erythromycin, azithromycin, clarithromycin
• Etc.
Developed within the past decade
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Antibiotic Resistance (con’t)
• Development of Multi-drug Resistance
– Variety of different mechanisms for bacterial mating
• Pheromone responsive plasmids
• Broad host-range plasmids
– Transfer among species of enterococci
• Conjugative transposons
– Transfer genetic information from cell to cell
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Vancomycin Resistance
•
•
•
•
Resistance to vancomycin unknown until 1986.
First vancomycin-resistant enterococcus found in France.
First strain isolated in 1987 in the United Kingdom.
Similar strains now found world-wide.
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How does vancomycin resistance arise?
• Genetic mechanism gives rise to resistance
– Models for phenotype evolution incorporating mutation,
selection, and recombination exist
– Mutation is typically modeled by diffusion
• Related antibiotics included in animal feed, resulting
in acquisition after ingestion
• Antibiotic therapy in hospitals
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Who is susceptible to VRE?
• Patients who have been in hospital for extended periods.
• Patients who have received certain antibiotics (vancomycin,
teicoplanin, cephalosporins).
• Patients fed by naso-gastric tube.
• Outbreaks primarily reported from renal dialysis, transplant,
haematology and ICUs.
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Vancomycin-Resistant Enterococci (VRE)
Treatment challenges
• Range of antibiotics available for treatment are extremely
limited.
• Choice of antibiotics for treatment dependent upon strain.
• Treatment delay due to time needed for laboratory results.
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Patient Dynamics
u0
UNCOLONIZED
length of stay
PATIENTS
u0
OFF ANTIBIOTICS
Pu0
new patients
admitted
u0
Start antibiotics
u1
Stop antibiotics
UNCOLONIZED
PATIENTS
ON ANTIBIOTICS
Pu1
u1
length of stay
u1
new patients
admitted
pp(1-) (Yh/Nh)
c0
COLONIZED
length of stay
PATIENTS
OFF ANTIBIOTICS
c0
Pc0
new patients
admitted
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c0
Start antibiotics
c1
Stop antibiotics
COLONIZED
PATIENTS
ON ANTIBIOTICS
Pc1
c1
length of stay
c1
new patients
admitted
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Health Care Worker Dynamics
p0h0 (Pc0/Np)
contamination from
colonized patients
on antibiotics
UNCONTAMINATED
HEALTH CARE
WORKERS
Hu
p1h1 (Pc1/Np)
contamination from
colonized patients
on antibiotics
CONTAMINATED
HEALTH CARE
WORKERS
Hc

length of contamination
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Epidemic Model for VRE in a Hospital
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Parameters of the Model
Parameter
Symbol
Value
Number of hospitalized patients
Np
400
Ratio of healthcare workers to patients

4
Number of uncolonized patients admitted / day
Off antibiotics
On antibiotics
Number of colonized patients admitted / day
Off antibiotics
On antibiotics
u0
u1
35
3
c0
c1
0.4
0.6
Length of hospital stay for
Uncolonized patients off antibiotics
Uncolonized patients on antibiotics
Colonized patients off antibiotics
Colonized patients on antibiotics
u0
u1
c0
c1
1/5 (5 days)
1/14 (14 days)
1/28 (28 days)
1/28 (28 days)
HCW contact rate / day
With uncolonized patients
With colonized patients
p0
p1
8
10
Probability of HCW hand contamination per contact
With uncolonized patients
With colonized patients
h0
h1
0.05
0.4
Probability of patient colonization per HCW contact
p1
0.06
Antibiotics started (% / day)
Uncolonized patients
Colonized patients
u0
c0
-log.85 ( 15% )
-log.84 ( 16% )
Antibiotics stopped (% / day)
Uncolonized patients
Colonized patients
u1
c1
-log.85 ( 15% )
-log.96 ( 4%)
Compliance with hand hygiene (between 0 and 1)

.5 (50%)
Duration of hand contamination

24 ( 1 hour)
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SIMULATIONS WITH VARIABLE
PATIENT-HCW RATIO
Patient-HCW ratios are  = 1 (red), 2 (green), 4 (blue), 6 (yellow) and 8 (purple)
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SIMULATIONS WITH VARIABLE
HYGIENE COMPLIANCE
Hygiene compliance values are  = .1 (red), .3 (green), .5 (blue), .7 (yellow) and .9 (purple)
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SIMULATIONS WITH VARIABLE ANTIBIOTIC
STOPPAGE OF COLONIZED PATIENTS
Per day discontinuation of antibiotics (c1) of VRE colonized patients =
4% (red), 7% (green), 10% (blue), 15% (yellow) and 20% (purple)
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SIMULATIONS WITH VARIABLE ANTIBIOTIC
STOPPAGE OF UNCOLONIZED PATIENTS
Per day discontinuation of antibiotics (u1) of VRE uncolonized patients =
4% (red), 7% (green), 10% (blue), 15% (yellow) and 20% (purple)
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SIMULATIONS WITH VARIABLE LENGTH OF STAY
OF COLONIZED PATIENTS ON ANTIBIOTICS
Length of hospital stay for VRE colonized patients on antibiotics (c1) =
10 days (red), 14 days (green), 21 days (blue), 28 days (yellow) and 35 days
(purple)
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SIMULATION OF THE MODEL WITH NO ADMISSIONS OF
COLONIZED PATIENTS (c0 = c1 =0)
All parameters have baseline values except that the handwashing
compliance  = 0 .7. The colonized patient compartments extinguish
over time.
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Vancomycin-Resistant Enterococci (VRE)
Preventing the spread of VRE--Conclusions
•
Restrict use of antibiotics, especially vancomycin, teicoplanin and
cephalosporins.
•
Enforce scrupulous handwashing by all hospital staff.
•
Lower the ratio of patients to health care workers.
•
Cohort colonized patients.
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Steady States of the Model (with c0 = c1 =0)
•
VRE Free Steady State
•
VRE Endemic Steady State
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Epidemic Model for VRE in a Hospital
Conclusions
•
If c0 and c1 are assumed to be 0, then R0 can be calculated for this
model (that is, there is no input of colonized patients either on or off
antibiotics).
•
R0 is the number of secondary infections produced by a single infective in a
new population of susceptibles.
If R0 is greater than 1, then VRE becomes endemic in the hospital. If R0 is
less than 1, then VRE extinguishes in the hospital.
If either c0 or c1 is assumed to be positive, then VRE always becomes
endemic.
•
•
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Epidemic Model for VRE in a Hospital
Conclusions
Lower patient-healthcare worker ratios limit the prevalence of patients
colonized with VRE (the benefit is less significant for higher ratios).
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Epidemic Model for VRE in a Hospital
Conclusions
Improved compliance with handwashing limits the prevalence of patients
colonized with VRE (the benefit is more significant for higher compliance
values).
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Epidemic Model for VRE in a Hospital
Conclusions
Starting unnecessary antimicrobial therapy has a greater impact when targeted
to patients who are not colonized with VRE, compared to patients colonized
with VRE
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Epidemic Model for VRE in a Hospital
Conclusions
Stopping unnecessary antimicrobial therapy has a greater impact when targeted
to patients who are not colonized with VRE, as compared to patients colonized
with VRE
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Epidemic Model for VRE in a Hospital
Conclusions
Prolonging the duration of hospitalization of colonized patients increases the
prevalence of VRE (but the increase is less significant for longer LOS) .
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Final Thoughts
Discouraging News
• First case of vancomycin-resistant Staphylococcus
aureus (VRSA) confirmed in 40-year-old Michigan
diabetic with kidney failure in July 2002
• In the U.S., methicillin-resistant Staphylococcus
aureus (MRSA) rates as high as 60% in some
facilities
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Final Thoughts
Hope for the Future
• Pharma companies working on veterinary phages that counter
E. coli and salmonella in animals are now moving into human
infections such as MRSA and VRE
• Immunization approaches under development
– Vaccine preventing middle ear infections in children on the market
– Clinical studies underway for an anti-MRSA vaccine called
StaphVac
– A TB vaccine is now being tested on animals that could counter the
multidrug-resistant strain now endemic in the third world
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