Cellular automata model for the transmission dynamics of antibiotic-resistant bacteria

The phenomenon of antibiotic resistance is of practical importance and theoretical interest. However, the link between antibiotic consumption and prevalence of resistance to a given drug has been difficult to establish for a variety of reasons. As a foundation for further studies by simulation, experiment and observation, we develop a probabilistic cellular automata model for the transmission dynamics and emergence of resistance among the bacteria resident in a population of human hosts, subject to varying levels of antibiotic treatment to control morbidity induced by pathogenic strains of normally commensal organism. Antibiotic treatment is independent of bacterial colonization, and a proportion of host individuals receive treatment at any time. The model incorporates the effects of natural selection within untreated hosts and the rapid increase of resistance in hosts who receive antibiotics. The analyses was performed in order to determine which of the strains wins the competition by the host. It is assumed that the eventual shift in the competition between the two strains is due to treatment by antibiotic (selective pressure). A peculiar characteristic of the present approach is the assumption that the probability of a susceptible individual become infective is a superposition of the local (contacts among nearest neighbors) and global (homogeneously interacting population) influences, which in turn can be tuned out to simulate respectively the populational mobility and geographycal neighborhood contacts. In the absence of antibiotic resistance, the model shows how the pattern of antibiotic control can eliminate the nonpathogenic commensal strains from the host community if the fraction of people taking antibiotics exceeds some critical level. Furthermore, the model is extended to take account of the evolution of antibiotic resistance in the commensal population and employed to address the issue of how best to use antibiotics in populations harboring resistant organisms. The predictions of the model are compared with those of other models and published data. The implications for resistance control and study design are discussed, along with the limitations and assumptions of the model. (Financial support: FAPESP, Proc. 02/03564-8 and 02/02190-7). (Subject Topic: Complexity, Dynamical Systems) REFERENCES[1]Austin, D. J., Kristinsson K. G, and Anderson, R. M. Therelationship between the volume of antimicrobialconsumption in human communities and the frequency ofresistance, Proc. Natl. Acad. Sci., vol. 96, pp.1152, 1999. [2]Massad, E., Ludberg S. and Yang, H. M. Modeling andsimulating the evolution of resistance against antibiotics, Int.J. Biomed. Comput., vol. 33, pp 65, 1993. [3]Alves, D. and Caliri, A. Epidemic propagation model and theevolution of antibiotic resistance, European Journal ofPharmaceutical Sciences, vol. 13, suppl. 1, s125, 2001. [4]Alves, D., Hass V. and Caliri, A. The predictive power of R0in an epidemic probabilistic model, Journal of BiologicalPhysics , vol. 29, issue 1 (2003).