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MODELING OUTBREAKS OF ANTIBIOTIC RESISTANCE IN HOSPITALS

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MODELING OUTBREAKS OF ANTIBIOTIC RESISTANCE IN HOSPITALS Erika D Agata, Beth Israel Deaconess Medical Center Harvard University Boston, MA, USA – PowerPoint PPT presentation

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Title: MODELING OUTBREAKS OF ANTIBIOTIC RESISTANCE IN HOSPITALS


1
MODELING OUTBREAKS OF ANTIBIOTIC RESISTANCE IN
HOSPITALS
Erika DAgata, Beth Israel Deaconess Medical
Center Harvard University Boston, MA, USA
Mary Ann Horn Mathematical Sciences
Division National Science Foundation Washington,
DC, USA
Pierre Magal Department of Mathematics Université
du Havre 76058 Le Havre, FRANCE
Damien Olivier Department of Computer
Sciences Université du Havre 76058 Le Havre,
FRANCE
Shigui Ruan Department of Mathematics University
of Miami Coral Gables, FL, USA
Glenn Webb Department of Mathematics Vanderbilt
University Nashville, TN USA
2
WHAT IS A NOSOCOMIAL INFECTION?
  • nos-o-co-mi-al adj originating or
    occurring in a hospital

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 21, 2002
3
WHY ARE NOSOCOMIAL INFECTIONS COMMON?
  • Hospitals house large numbers of people whose
    immune systems are often in a weakened state.
  • Increased use of outpatient treatment means that
    patients in the hospital are more vunerable.
  • Medical staff move from patient to patient,
    providing a way for pathogens to spread.
  • Many medical procedures bypass the body's natural
    protective barriers.

4
A GROWING PROBLEM
  • Approximately 10 of U.S. hospital patients
    (about 2 million every year) acquire a clinically
    significant nosocomial infection.
  • Nosocomial infections are responsible for about
    100,000 deaths per year in hospitals
  • More than 70 percent of bacteria that cause
    hospital-acquired infections are resistant to at
    least one of the drugs most commonly used in
    treatment

5
Methicillin (oxacillin)-resistant Staphylococcus
aureus (MRSA) Among ICU Patients, 1995-2004
Source National Nosocomial Infections
Surveillance (NNIS) System
6
Vancomycin-resistant Enteroccoci (VRE) Among
ICU Patients,1995-2004
Source National Nosocomial Infections
Surveillance (NNIS) System
7
WHAT IS THE CONNECTION OF ANTIBIOTIC USE TO
NOSOCOMIAL EPIDEMICS?
  • High prevalence of resistant bacterial strains
    present in the
  • hospital
  • High capacity of bacteria to mutate to resistant
    strains
  • Selective advantage of mutant strains during
    antibiotic therapy
  • Misuse and overuse of antibiotics
  • Medical practice focused on individual patients
    rather than the general hospital patient
    community

8
TYPES OF MICROBIAL RESISTANCE TO ANTIBIOTICS
  • Inherent - microorganisms may be resistant to
    antibiotics because of physical and biochemical
    differences.
  • Acquired - bacteria can develop resistance to
    antibiotics driven by two genetic processes
  • (a) mutation and selection (vertical evolution)
  • (b) exchange of genes (plasmids) between strains
    and species (horizontal evolution).

9
OBJECTIVES OF THE MODELING PROJECT
  • Construct a model based on observable hospital
    parameters, focusing on healthcare worker (HCW)
    contamination by patients, patient infection by
    healthcare workers, and infectiousness of
    patients undergoing antibiotic therapy.
  • Analyze the elements in the model and determine
    strategies to mitigate nosocomial epidemics

10
THE TWO LEVELS OF A NOSOCOMIAL EPIDEMIC
  • Bacteria population level in a single infected
    host
  • (i) host infected with the nonresistant
    strain
  • (ii) host infected with the resistant
    strain
  • Patient and healthcare worker level in the
    hospital
  • (i) uninfected patients susceptible to
    infection
  • (ii) patients infected with the
    nonresistant strain
  • (iii) patients infected with the
    resistant strain
  • (iv) uncontaminated HCW
  • (v) contaminated HCW

11
AN ORDINARY DIFFERENTIAL EQUATIONS MODEL AT THE
BACTERIA POPULATION LEVEL
  • A. Bacteria in a host infected only with the
    nonresistant strain
  • VF(a) population of nonresistant bacteria at
    infection age a
  • ?F(a) proliferation rate
  • ?F carrying capacity parameter of the host
  • B. Bacteria in a host infected with both
    nonresistant and resistant strains
  • V?(a) population of nonresistant bacteria at
    infection age a
  • V?(a) population of resistant bacteria at
    infection age a
  • V(a) V?(a) V?(a)
  • ???????????????????????_(a)?????(a)
    proliferation rates
  • ?????????????????????? recombination rate, ??
    reversion rate

12
MODEL OF PLASMID FREE BACTERIA IN A SINGLE
INFECTED HOST INFECTED WITH ONLY PLASMID FREE
BACTERIA
If ?F gt0, then lima??VF(a)?F if ?Flt0, then
lima??VF(a)0.
bF12.0?log(2) before treatment (doubling time
2 hr), bF-2.0 after treatment, kF1010.
13
MODEL OF BACTERIA IN A SINGLE INFECTED HOST
INFECTED WITH PLASMID FREE AND PLASMID BEARING
BACTERIA
Equilibria of the model E0 (0,0), EF (?F
???0), and
14
MODEL OF ANTIBIOTIC TREATMENT IN A SINGLE
INFECTED HOST - TRACKING THE BACTERIAL LOAD
Treatment starts at day 3 and lasts 21 days
Treatment starts at day 5 and lasts 14 days
15
AN INDIVIDUAL BASED MODEL (IBM) AT THE HOSPITAL
POPULATION LEVEL
  • Three stochastic processes
  • the admission and exit of patients
  • the infection of patients by HCW
  • the contamination of HCW by patients

These processes occur in the hospital over a
period of months or years as the epidemic evolves
day by day. Each day is decomposed into 3 shifts
of 8 hours for the HCW. Each HCW begins a shift
uncontaminated, but may become contaminated
during a shift. During the shift a time step ?t
delimits the stochastic processes. The bacterial
load of infected patients during antibiotic
treatment is monitored in order to describe the
influence of treatment on the infectiousness of
patients.
16
PATIENT AND HCW POPULATION LEVEL
Top Healthare workers are divided into four
classes uncontaminated (HU), contaminated only
with non-resistant bacteria (HN), contaminated
with both non-resistant and resistant bacteria
(HNR), and contaminated only with resistant
bacteria (HR) Bottom Patients are divided into
five classes uninfected patients (PU), patients
infected only by the non-resistant strain (PN),
and three classes of patients infected by
resistant bacteria (PRS), (PNR), and (PRR). PRS
consists of super-infected patients, that is,
patients that were in class PN and later become
infected with resistant bacteria. PRR consists of
patients that were uninfected and then became
infected by resistant bacteria. PNR consists of
patients that were uninfected, and then become
infected with both non-resistant and resistant
bacteria.
17
INFECTIOUSNESS OF INDIVIDUAL PATIENTS
Infectiousness periods when the antibiotic
treatment starts on day 3 and stops on day 21
(inoculation occurs on day 0). The blue and red
curves represent, respectively, the bacterial
load of resistant and non-resistant bacteria
during the period of infection. The green
horizontal lines represent the threshold of
infectiousness TH1011. The green bars represent
the treatment period. The yellow, red, and orange
bars represent the periods of infectiousness for
the non-resistant, resistant, and both
non-resistant and resistant classes,
respectively.
18
PARAMETERS OF THE IBM AT THE HOSPITAL LEVEL
Beth Israel Deaconess Medical Center, Harvard,
Boston Cook County Hospital, Chicago
19
THE INFECTION AND CONTAMINATION PROCESSES
Patient-HCW contact diagram for 4 patients and 1
HCW during one shift. Patient status uninfected
(green), infected with the non-resistant strain
(yellow), infected with the resistant strain
(red). HCW status uncontaminated (______ ),
contaminated with the non-resistant strain (),
contaminated with the resistant strain (- - - - -
).
20
SUMMARY OF THE IBM MODEL ASSUMPTIONS
  • each HCW begins the first visit of the shift
    uncontaminated and subsequent patient visits are
    randomly chosen among patients without a HCW
  • at the end of a visit a HCW becomes contaminated
    from an infectious patient with probability PC
    and a patient becomes infected from a
    contaminated HCW with probability PI
  • the bacterial load of an infected patient is
    dependent on treatment scheduling and infected
    patients are infectious to a HCW when their
    bacterial load is above a threshold TH
  • each time step ?t a contaminated HCW exits
    contamination with probability 1 - exp(-?t/AC)
    (AC average period of contamination) and exits
    a visit with probability 1 - exp(-?t/AV) (AV
    average length of visit)
  • each time step ?t a patient of type L exits the
    hospital with probability
  • 1 - exp(-?t/AL), where AL average
    length of stay and L U,N,R.
  • (vi) The number of patients in the hospital is
    assumed constant, so that a patient leaving the
    hospital is immediately replace by a new patient
    in class (U).

21
TWO SIMULATIONS OF THE IBM WITH DIFFERENT
TREATMENT SCHEDULES
From the two IBM simulations we see that when
treatment starts earlier and has a shorter
period, both non-resistant and resistant strains
are eliminated. Earlier initiation of treatment
reduces the non-resistant bacterial load and
shorter treatment intervals reduce the time that
patients infected by the resistant strain are
infectious for this strain.
22
A COMPLEMENTARY DIFFERENTIAL EQUATIONS MODEL
(DEM)
The Individual Based Model (IBM) provides a
stochastic simulation of the epidemic based on
probabilistic assumptions on events occurring in
the hospital. But the IBM is different every time
it is simulated, and it is difficult to analyse
the effects of various elements in the model. For
example, what is the effect of modify the length
of HCW contamination periods or the length of
treatment periods? We develop a Differential
Equations Model (DEM) that corresponds to the
average behavior of the IBM over a large number
of simulations. The DEM is based on dynamic rates
of change of the processes occurring over the
course of the epidemic.
23
KEY PARAMETERS OF THE DEM
24
EQUATIONS OF THE DEM
25
EQUATIONS FOR THE HEALTHCARE WORKERS
The equations for the HCW are motivated by a
singular perturbation technique. The idea is
that the time scale of the HCW is much smaller
than the time scale for the evolution of the
epidemic at the patient level. These equations
are solved for the HCW fractions.
26
EQUATIONS FOR THE FRACTIONS OF PATIENTS
INFECTIOUS FOR THE BACTERIAL STRAINS
27
COMPARISON OF THE IBM AND THE DEM
Beginning of treatment day 3 End of treatment
day 21
Beginning of treatment day 1 End of treatment
day 8
28
ANALYSIS OF THE PARAMETRIC INPUT
A major advantage of the DEM is that the
parametric input can be analyzed in terms of the
parametric input. This is accomplished by
calculating R0 epidemic basic reproductive
number. R0 predicts the expected number of
secondary cases per primary case. When R0 lt1,
then the epidemic extinguishes and when R0 gt1,
then the epidemic becomes endemic. R0 is a
function of all the parameters in the model, and
a sensitivity analysis of R0 can be carried out
by holding some of the parameters fixed and
varying some of the other parameters.
29
EFFECTS OF CHANGING THE DAY TREATMENT BEGINS AND
HOW LONG IT LASTS
R0Rlt1 or R0Rgt1 depending on the starting day and
the duration of treatment. R0R is increasing when
the starting day of treatment increases, because
the bacterial loads of both strains are higher if
treatment is delayed and thus more likely to
reach threshold Further, R0R increases as the
length of treatment duration increases, because
the resistant strain prevails during treatment.
30
EFFECTS OF CHANGING THE LENGTH OF VISITS AND THE
LENGTH OF CONTAMINATION OF HCW
R0Rlt1 or R0Rgt1 depending on the length of HCW
visits and the length of HCW contamination. R0R
decreases as the length of visits AC increases
and increase as the length of contamination AV
increases, but the dependence is linear in AC and
quadratic in 1/AV. The reason is AC is specific
to HCW, but AV is specific to both HCW and
patients.
31
CONCLUSIONS OF THE MODEL
  • Antibiotic therapy regimens should balance the
    care of individual patients and the general
    patient population welfare.
  • Antibiotic treatment should start as soon as
    possible
  • after infection is diagnosed and its duration
    should be minimized.
  • Mathematical models can create virtual hospitals
    and analyze measures to control nosocomial
    epidemics (hospital acquired infection epidemics)
    in specific hospital environments.

32
REFERENCES
E. DAgata, M.A. Horn, and G.F. Webb, The impact
of persistent gastrointestinal colonization on
the transmission dynamics of vancomycin-resistant
enterococci, J. Infect. Dis. ,Vol. 185 (2002),
766-773. E. DAgata, M.A. Horn, and G.F. Webb, A
mathematical model quantifying the impact of
antibiotic exposure and other interventions on
the endemic prevalence of vancomycin-resistant
enterococci, J. Infect. Dis., Vol. 192 (2005),
2004-2011. E. DAgata, P. Magal, S. Ruan, and
G.F. Webb, A model of antibiotic resistant
bacterial epidemics in hospitals, Proc. Nat.
Acad. Sci. Vol. 102, No. 37, (2005),
13343-13348. E. D'Agata, P. Magal, S. Ruan, and
G.F. Webb, Modeling antibiotic resistance in
hospitals The impact of minimizing treatment
duration, J. Theoret. Biol., Available online
Aug. 27 (2007).
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