Mathematical models for interventions on drug resistance
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Mathematical models for interventions on drug resistance. Hsien-Ho Lin. Motivation….

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The first model builders in tuberculosis met with considerable opposition from those who maintained that many essential parameters were not established with sufficient precision, although paradoxically, those very opponents apparently had their own intuitive models on which to base highly assertive decisions.

World Health Organization, 1973

cited by Lietman and Blower CID 2000


Which interventional strategies are possible
Which interventional strategies are possible? considerable opposition from those who maintained that many essential parameters were not established with sufficient precision, although paradoxically, those very opponents apparently had their own intuitive models on which to base highly assertive decisions.

  • Cycling

  • “Search and destroy”

  • Rapid diagnostic testing

  • Antibiotic restriction

  • Education interventions/campaigns

  • Antibiotic combinations

  • Short course/higher doses


How to choose between alternative strategies
How to choose between alternative strategies? considerable opposition from those who maintained that many essential parameters were not established with sufficient precision, although paradoxically, those very opponents apparently had their own intuitive models on which to base highly assertive decisions.

  • Requires:

    • Clearly stated goal(s) of control

    • A method to compare the ability interventions to meet these goals

  • How to compare the performance of interventions?

    • Observation

    • Quasi-experimental

    • Experiment / Clinical trials

    • Model


Challenges
Challenges considerable opposition from those who maintained that many essential parameters were not established with sufficient precision, although paradoxically, those very opponents apparently had their own intuitive models on which to base highly assertive decisions.

  • Observational study

    • Baseline differences / Confounding

    • Individual / group level effect

    • Time trend / stage of epidemics

  • Clinical trial: randomized study

    • Long enough duration to detect delayed effects

    • Many possible interventions to be tested

    • Ethical limitations

  • Models


What is a model
What is a model? considerable opposition from those who maintained that many essential parameters were not established with sufficient precision, although paradoxically, those very opponents apparently had their own intuitive models on which to base highly assertive decisions.

  • Simplified representation of a more complex system

  • Goal:

    • Develop a model which omits details which do not affect the behavior of the system

    • Model will reflect both the system studied and the question asked

  • Why create a model?

    • Complex systems are difficult to understand

    • We all use models, here we are formalizing


How do we decide what to omit
How do we decide what to omit? considerable opposition from those who maintained that many essential parameters were not established with sufficient precision, although paradoxically, those very opponents apparently had their own intuitive models on which to base highly assertive decisions.

  • Develop candidate model(s) which includes only those details that we think to be essential

    • for the natural history of disease

    • for the interventions we intend to simulate

  • Our knowledge of natural history and disease trends help determine parameter values and inform the structure of a model

    • but do not do so uniquely!


Case study i
Case study I considerable opposition from those who maintained that many essential parameters were not established with sufficient precision, although paradoxically, those very opponents apparently had their own intuitive models on which to base highly assertive decisions.

  • Modeling the impact of antibiotic cycling


Fig. 1. Schematic diagram of the model and the corresponding differential equations

β=1

c=0

γ=0.03

m=0.7

m1=.05

m2=.05

τ1+τ2=0.5

μ=0.1

σ=.25

α=0.8

Bergstrom, Carl T. et al. (2004) Proc. Natl. Acad. Sci. USA 101, 13285-13290


Fig. 3-4. Fraction of patients carrying resistant bacteria, for cycle lengths of 1 yr, 3 months, and 2 weeks, respectively

Bergstrom, Carl T. et al. (2004) Proc. Natl. Acad. Sci. USA 101, 13285-13290


A bug’s view for cycle lengths of 1 yr, 3 months, and 2 weeks, respectively

Bergstrom, Carl T. et al. (2004) Proc. Natl. Acad. Sci. USA 101, 13285-13290


Authors conclusion
Authors’ conclusion for cycle lengths of 1 yr, 3 months, and 2 weeks, respectively

  • Cycling is unlikely to be effective and may even hinder resistance control


Hm….. for cycle lengths of 1 yr, 3 months, and 2 weeks, respectively

  • Model structure

    • Mixed colonization?

  • Parameter values

  • Constant rate assumption

    • A strain never totally dies out

  • Homogeneous mixing


Case study ii
Case study II for cycle lengths of 1 yr, 3 months, and 2 weeks, respectively

  • Modeling the impact of “search and destroy” and rapid diagnostic testing


Search and destroy
Search and destroy for cycle lengths of 1 yr, 3 months, and 2 weeks, respectively


Fig. 1. Patient dynamics (a) and MRSA dynamics (b) within a hospital

Bootsma, M. C. J. et al. (2006) Proc. Natl. Acad. Sci. USA 103, 5620-5625


Fig. 3. Effect of intervention strategies on nosocomial prevalence levels when isolation is 100% effective

Bootsma, M. C. J. et al. (2006) Proc. Natl. Acad. Sci. USA 103, 5620-5625


Fig. 4. Changes in critical reproduction ratio (R0c) for several combinations of intervention measures according to changes in model parameters

Bootsma, M. C. J. et al. (2006) Proc. Natl. Acad. Sci. USA 103, 5620-5625


Authors conclusions
Authors’ conclusions several combinations of intervention measures according to changes in model parameters

  • ……

  • MRSA-prevalence can be reduced to <1% (within 6 years) in high-endemic settings by S&D

  • …..

  • RDT can reduce isolation needs by >90% in low-endemic settings and by 20% in high-endemic settings

  • ???


Challenges for developing models for assessing interventions for drug resistance
Challenges for developing models for assessing interventions for drug resistance

“…as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns -- the ones we don't know we don't know."

Donald Rumsfeld

Former US Secretary of Defense


Known knowns
Known knowns for drug resistance

  • Colonization occurs after exposure to colonized patients

  • A hospital is an open system

  • People can enter a hospital colonized with the pathogen of interest

  • Antibiotics used at a much higher rate in the hospital

  • Spontaneous clearance of colonization


Known unknowns
Known unknowns for drug resistance

  • Fitness cost of being resistant

  • Supercolonization

  • Importance of mixed colonization; within-host competition between strains under different scenarios of selection pressure

  • Details of transmission where assumptions of homogeneity break down

  • Unanticipated human, pathogen, environmental behavior

  • What changes will occur as epidemic progresses and interventions are implemented?


Unknown unknowns
Unknown unknowns for drug resistance

  • Unanticipated consequences of interventions

    • Synergistic

    • Antagonistic


Caveat
Caveat for drug resistance

  • We should expect that the lists of known unknowns and unknown unknowns are longer than the first list

  • Should give us pause about our ability to accurately project disease trends into the future


Conclusions
Conclusions for drug resistance

  • We need models to help form interventional strategies against antibiotic resistance (we have few reasonable alternatives)

  • These models reflect both our knowledge and ignorance of the essential processes underlying the transmission dynamics of pathogens within hospitals/communities

  • These models will inform us of the most important areas for further research

  • These models should allow us to rank categories of interventions in their probable impact on our chosen outcome

  • However, precise quantification of impact of interventions is too much to ask of these crude tools


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