Optimal strategies in antibiotic treatment of microbial populations

Abstract

The well-known fact is that bacterial populations can be resistant to the antibiotic treatment. We formulate a mathematical model that takes this fact into account. The model describes two microbial populations (susceptible and persister cells), a nutrient, and an antibiotic. The susceptible cells can be affected by antibiotic. The complexity of the problem is that we cannot give the antibiotic to the patient all the time during the treatment process, since in this case the population of the persister cells will grow. Therefore, we aimed to find a special balance in providing the antibiotic. To achieve this, the optimal control theory was used to find successful treatment strategies. A discontinuous problem with receiving the antibiotic several times a day at regular intervals was also considered and the corresponding successful strategies were found. Moreover, the problem with the constraint on the total concentration of the antibiotic was investigated, however it turns out that this restriction does not change significantly the principle of the system control.

Keywords:

• Antibiotic treatment
• bacterial persistence
• optimal control strategies
• numerical methods for optimal systems

AMS Subject Classifications:

• 92

Notes

No potential conflict of interest was reported by the authors.