Abstract
Biofilms are heterogeneous matrix enclosed micro-colonies of bac-teria mostly found on moist surfaces. Biofilm formation is the primary cause of several persistent infections found in humans. We derive a mathematical model of biofilm and surrounding fluid dynamics to investigate the effect of a periodic dose of antibiotic on elimination of microbial population from biofilm. The growth rate of bacteria in biofilm is taken as Monod type for the limiting nutrient. The pharmacodynamics function is taken to be dependent both on limiting nutrient and antibiotic concentration. Assuming that flow rate of fluid compartment is large enough, we reduce the six dimensional model to a three dimensional model. Mathematically rigorous results are derived providing suf-ficient conditions for treatment success. Persistence theory is used to derive conditions under which the periodic solution for treatment failure is obtained. We also discuss the phenomenon of bi-stability where both infection-free state and infection state are locally stable when antibiotic dosing is marginal. In addition, we derive the optimal antibiotic application protocols for different scenarios using control theory and show that such treatments ensure bacteria elimination for a wide variety of cases. The results show that bacteria are successfully eliminated if the discrete treatment is given at an early stage in the infection or if the optimal protocol is adopted. Finally, we examine factors which if changed can result in treatment success of the previously treatment failure cases for the non-optimal technique.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 547-571 |
| Number of pages | 25 |
| Journal | Mathematical Biosciences and Engineering |
| Volume | 11 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jun 2014 |
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Keywords
- Antibiotic treatment
- Bactericidal
- Biofilm
- Persistence
- Perturbation
- Stability
ASJC Scopus subject areas
- Applied Mathematics
- Modeling and Simulation
- Computational Mathematics
- Agricultural and Biological Sciences(all)
- Medicine(all)
Cite this
A model of optimal dosing of antibiotic treatment in biofilm. / Imran, Mudassar; Smith, Hal.
In: Mathematical Biosciences and Engineering, Vol. 11, No. 3, 06.2014, p. 547-571.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A model of optimal dosing of antibiotic treatment in biofilm
AU - Imran, Mudassar
AU - Smith, Hal
PY - 2014/6
Y1 - 2014/6
N2 - Biofilms are heterogeneous matrix enclosed micro-colonies of bac-teria mostly found on moist surfaces. Biofilm formation is the primary cause of several persistent infections found in humans. We derive a mathematical model of biofilm and surrounding fluid dynamics to investigate the effect of a periodic dose of antibiotic on elimination of microbial population from biofilm. The growth rate of bacteria in biofilm is taken as Monod type for the limiting nutrient. The pharmacodynamics function is taken to be dependent both on limiting nutrient and antibiotic concentration. Assuming that flow rate of fluid compartment is large enough, we reduce the six dimensional model to a three dimensional model. Mathematically rigorous results are derived providing suf-ficient conditions for treatment success. Persistence theory is used to derive conditions under which the periodic solution for treatment failure is obtained. We also discuss the phenomenon of bi-stability where both infection-free state and infection state are locally stable when antibiotic dosing is marginal. In addition, we derive the optimal antibiotic application protocols for different scenarios using control theory and show that such treatments ensure bacteria elimination for a wide variety of cases. The results show that bacteria are successfully eliminated if the discrete treatment is given at an early stage in the infection or if the optimal protocol is adopted. Finally, we examine factors which if changed can result in treatment success of the previously treatment failure cases for the non-optimal technique.
AB - Biofilms are heterogeneous matrix enclosed micro-colonies of bac-teria mostly found on moist surfaces. Biofilm formation is the primary cause of several persistent infections found in humans. We derive a mathematical model of biofilm and surrounding fluid dynamics to investigate the effect of a periodic dose of antibiotic on elimination of microbial population from biofilm. The growth rate of bacteria in biofilm is taken as Monod type for the limiting nutrient. The pharmacodynamics function is taken to be dependent both on limiting nutrient and antibiotic concentration. Assuming that flow rate of fluid compartment is large enough, we reduce the six dimensional model to a three dimensional model. Mathematically rigorous results are derived providing suf-ficient conditions for treatment success. Persistence theory is used to derive conditions under which the periodic solution for treatment failure is obtained. We also discuss the phenomenon of bi-stability where both infection-free state and infection state are locally stable when antibiotic dosing is marginal. In addition, we derive the optimal antibiotic application protocols for different scenarios using control theory and show that such treatments ensure bacteria elimination for a wide variety of cases. The results show that bacteria are successfully eliminated if the discrete treatment is given at an early stage in the infection or if the optimal protocol is adopted. Finally, we examine factors which if changed can result in treatment success of the previously treatment failure cases for the non-optimal technique.
KW - Antibiotic treatment
KW - Bactericidal
KW - Biofilm
KW - Persistence
KW - Perturbation
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84894235889&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84894235889&partnerID=8YFLogxK
U2 - 10.3934/mbe.2014.11.547
DO - 10.3934/mbe.2014.11.547
M3 - Article
C2 - 24506551
AN - SCOPUS:84894235889
VL - 11
SP - 547
EP - 571
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
SN - 1547-1063
IS - 3
ER -