Mathematical Modelling and Challenges in the Development of Drug Resistance

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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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### 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?

• 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

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

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

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.
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
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.

Antibiotic Resistance (con’t)
• Development of Multi-drug Resistance
• Variety of different mechanisms for bacterial mating
• Pheromone responsive plasmids
• Transfer among species of enterococci
• Conjugative transposons
• Transfer genetic information from cell to cell
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.
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
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.
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.
Patient Dynamics

u0

u0

UNCOLONIZED

PATIENTS

OFF ANTIBIOTICS

Pu0

UNCOLONIZED

PATIENTS

ON ANTIBIOTICS

Pu1

u1

length of stay

Start antibiotics

length of stay

u0

u1

u1

new patients

Stop antibiotics

new patients

pp(1-) (Yh/Nh)

COLONIZED

PATIENTS

OFF ANTIBIOTICS

Pc0

c0

COLONIZED

PATIENTS

ON ANTIBIOTICS

Pc1

c0

c1

Start antibiotics

length of stay

length of stay

c1

c1

c0

Stop antibiotics

new patients

new patients

Health Care Worker Dynamics

UNCONTAMINATED

HEALTH CARE

WORKERS

Hu

p0h0 (Pc0/Np)

CONTAMINATED

HEALTH CARE

WORKERS

Hc

contamination from

colonized patients

on antibiotics

p1h1 (Pc1/Np)

contamination from

colonized patients

on antibiotics

length of contamination

SIMULATIONS WITH VARIABLE PATIENT-HCW RATIO

Patient-HCW ratios are  = 1 (red), 2 (green), 4 (blue), 6 (yellow) and 8 (purple)

SIMULATIONS WITH VARIABLE HYGIENE COMPLIANCE

Hygiene compliance values areh= .1 (red), .3 (green), .5 (blue), .7 (yellow) and .9 (purple)

Per day discontinuation of antibiotics (sc1) of VRE colonized patients =

4% (red), 7% (green), 10% (blue), 15% (yellow) and 20% (purple)

Per day discontinuation of antibiotics (su1) of VRE uncolonized patients =

4% (red), 7% (green), 10% (blue), 15% (yellow) and 20% (purple)

SIMULATIONS WITH VARIABLE LENGTH OF STAY OF COLONIZED PATIENTS ON ANTIBIOTICS

Length of hospital stay for VRE colonized patients on antibiotics (gc1) =

10 days (red), 14 days (green), 21 days (blue), 28 days (yellow) and 35 days (purple)

SIMULATION OF THE MODEL WITH NO ADMISSIONS OF COLONIZED PATIENTS (c0 = c1 =0)

All parameters have baseline values except that the handwashing complianceh = 0 .7. The colonized patient compartments extinguish over time.

Vancomycin-Resistant Enterococci (VRE)

• 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.
Steady States of the Model (with c0 = c1 =0)
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.
Epidemic Model for VRE in a HospitalConclusions

Lower patient-healthcare worker ratios limit the prevalence of patients

colonized with VRE (the benefit is less significant for higher ratios).

Epidemic Model for VRE in a HospitalConclusions

Improved compliance with handwashing limits the prevalence of patients colonized with VRE (the benefit is more significant for higher compliance values).

Epidemic Model for VRE in a HospitalConclusions

Starting unnecessary antimicrobial therapy has a greater impact when targeted to patients who are not colonized with VRE, compared to patients colonized with VRE

Epidemic Model for VRE in a HospitalConclusions

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

Epidemic Model for VRE in a HospitalConclusions

Prolonging the duration of hospitalization of colonized patients increases the prevalence of VRE (but the increase is less significant for longer LOS) .

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
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