vanderbilt university department of mathematics mathematical modelling and challenges in the...

Vanderbilt UniversityVanderbilt UniversityDepartment of MathematicsDepartment of Mathematics

Mathematical Modelling and Mathematical Modelling and Challenges in the Development Challenges in the Development

of Drug Resistanceof Drug Resistance

Mary Ann Horn


Joint work with Erika D’Agata, Harvard Medical School and Glenn Webb, Vanderbilt University

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Enterococci

What are enterococci?

• 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

Photo credit: University of Oklahoma Health Sciences Center

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Nosocomial Infections

What does “nosocomial” mean?

-- Michael J. Berens, Chicago Tribune, July 22, 2002

“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.”

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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

UNCOLONIZEDPATIENTS

OFF ANTIBIOTICSPu0

COLONIZEDPATIENTS

OFF ANTIBIOTICSPc0

UNCOLONIZEDPATIENTS

ON ANTIBIOTICSPu1

COLONIZEDPATIENTS

ON ANTIBIOTICSPc1

u0

pp(1-) (Yh/Nh)

u1

u1

u0

new patientsadmitted


c0

c0

u0

Start antibiotics

Stop antibiotics

u1

c1

c1



length of stay

length of stay

length of stay

length of stay Start antibiotics

c0

c1

Stop antibiotics

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Health Care Worker Dynamics

UNCONTAMINATEDHEALTH CARE

WORKERSHu

CONTAMINATEDHEALTH CARE

WORKERSHc

p1h1 (Pc1/Np)

contamination fromcolonized patients

on antibiotics

length of contamination

contamination fromcolonized patients

on antibiotics

p0h0 (Pc0/Np)

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Epidemic Model for VRE in a Hospital

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Parameters of the ModelParameter Symbol Value

Number of hospitalized patients Np 400

Ratio of healthcare workers to patients 4

Numbe r o f uncolonize d patients admitte d / dayOff antibioticsOn antibiotics

u0u1

35 3

Numbe r o f colonize d patient s admitt ed / dayOff antibioticsOn antibiotics

c0c1

0.40.6

Length of hospita l sta y forUncolonize d patient s off antibioticsUncolonize d patient s on antibioticsColonize d patient s off antibioticsColonize d patient s on antibiotics

u0u1c0c1

1/5 (5 days)1/14 (14 days)1/28 (28 days)1/28 (28 days)

HCW contact rate / dayWit h uncolonize d patientsWith coloniz ed patients

p0p1

810

Probability of H CW han d contaminatio n pe r contactWit h uncolonize d patientsWit h colonize d patients

Probability of patien t colonizatio n pe r HCW contact

h0h1

p1

0.050.4

0.06Antibiotics starte d (% / day)

Uncoloni zed patientsColonize d patients

u0c0

-log.85 (15%)-log.84 (16%)

Antibiotics stop (ped % / day)Uncoloni zed patientsColonize d patients

u1c1

-log.85 (15%)-log.96 (4%)

Complianc e with ha nd hygien e (betwee 0 n a 1nd ) .5 (50% )

Durati on of ha nd 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 ANTIBIOTICSTOPPAGE 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 ANTIBIOTICSTOPPAGE 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 HospitalConclusions

• 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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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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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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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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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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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

vanderbilt university department of mathematics mathematical modelling and challenges in the...

Documents

vanderbilt university

cell slide

inherent resistance

resistance genes

nosocomial infections

enterococci issues

types of enterococci

past decade slide