Mathematical Model of Plasmid-Mediated Resistance to Ceftiofur in Commensal Enteric Escherichia coli of Cattle

Antimicrobial use in food animals may contribute to antimicrobial resistance in bacteria of animals and humans. Commensal bacteria of animal intestine may serve as a reservoir of resistance-genes. To understand the dynamics of plasmid-mediated resistance to cephalosporin ceftiofur in enteric commensals of cattle, we developed a deterministic mathematical model of the dynamics of ceftiofur-sensitive and resistant commensal enteric Escherichia coli (E. coli) in the absence of and during parenteral therapy with ceftiofur. The most common treatment scenarios including those using a sustained-release drug formulation were simulated; the model outputs were in agreement with the available experimental data. The model indicated that a low but stable fraction of resistant enteric E. coli could persist in the absence of immediate ceftiofur pressure, being sustained by horizontal and vertical transfers of plasmids carrying resistance-genes, and ingestion of resistant E. coli. During parenteral therapy with ceftiofur, resistant enteric E. coli expanded in absolute number and relative frequency. This expansion was most influenced by parameters of antimicrobial action of ceftiofur against E. coli. After treatment (>5 weeks from start of therapy) the fraction of ceftiofur-resistant cells among enteric E. coli, similar to that in the absence of treatment, was most influenced by the parameters of ecology of enteric E. coli, such as the frequency of transfer of plasmids carrying resistance-genes, the rate of replacement of enteric E. coli by ingested E. coli, and the frequency of ceftiofur resistance in the latter

Bayes Factor ratios comparing each model of Hansen’s Disease, by region of Brazil, as fitted by Approximate Bayesian Computation.

<p>Each value is a pairwise comparison of the strength of evidence for the fitted model (row) against a comparative model (column). Values in bold were considered strongly in favor of the model represented in that row over the comparative model, while values in italics are considered weak.</p><p>Bayes Factor ratios comparing each model of Hansen’s Disease, by region of Brazil, as fitted by Approximate Bayesian Computation.</p

Posterior distribution median and 95% prediction intervals determined by ABC fitting of Approximate Bayesian Computation models for Hansen’s Disease to data from the 5 regions of Brazil.

<p>Version 4 consisted of fitting the regional best-fit model to each region’s observed data separately; all other versions used a hierarchical structure in which at least some parameters were shared across regions, and fitting was done simultaneously across all 5 regions. Relative weight refers to the Bayes Factor of each version when compared to the version with the worst fit (Version 3).</p><p>^aVersion of the hierarchical structure sharing parameters across 5 regions of Brazil: 1) all parameters shared; 2) transmission parameters shared; 3) transition parameters shared; 4) no parameters shared</p><p>Posterior distribution median and 95% prediction intervals determined by ABC fitting of Approximate Bayesian Computation models for Hansen’s Disease to data from the 5 regions of Brazil.</p

Use of Approximate Bayesian Computation to Assess and Fit Models of <i>Mycobacterium leprae</i> to Predict Outcomes of the Brazilian Control Program

<div><p>Hansen’s disease (leprosy) elimination has proven difficult in several countries, including Brazil, and there is a need for a mathematical model that can predict control program efficacy. This study applied the Approximate Bayesian Computation algorithm to fit 6 different proposed models to each of the 5 regions of Brazil, then fitted hierarchical models based on the best-fit regional models to the entire country. The best model proposed for most regions was a simple model. Posterior checks found that the model results were more similar to the observed incidence after fitting than before, and that parameters varied slightly by region. Current control programs were predicted to require additional measures to eliminate Hansen’s Disease as a public health problem in Brazil.</p></div

Posterior checks for the incidence of multibacillary Hansen’s Disease in the 5 regions of Brazil.

<p>Observed incidence (black solid line) is shown with estimated incidence from Model 3 fitted hierarchically (purple dashed lines) and regionally (blue solid lines) and unfitted (brown dot-dash line). In the hierarchical model, parameters were fitted across all regions.</p

Posterior checks for the incidence of paucibacillary Hansen’s Disease in the 5 regions of Brazil.

<p>Observed incidence (black solid line) is shown with estimated incidence from Model 3 fitted hierarchically (purple dashed lines) and regionally (blue solid lines) and unfitted (brown dot-dash line). In the hierarchical model, parameters were fitted across all regions.</p

Regional incidence observations (cases per 10,000) used to fit models of Hansen’s Disease in Brazil.

<p>PB: paucibacillary</p><p>MB: multibacillary</p><p>Regional incidence observations (cases per 10,000) used to fit models of Hansen’s Disease in Brazil.</p

Assumptions made about the initial number of individuals per category and the calculation of incidence for 6 models of Hansen’s Disease.

<p>PB: paucibacillary</p><p>MB: multibacillary</p><p>N: regional population size</p><p>C: number of cases expected (N*prev)</p><p>prev: reported regional prevalence in 2000</p><p>P(MB): observed regional probability that a new case is multibacillary</p><p>π_i: relationship between C and the initial number of individuals in the <i>i</i> compartment (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0129535#pone.0129535.s003" target="_blank">S1 File</a>)</p><p>Assumptions made about the initial number of individuals per category and the calculation of incidence for 6 models of Hansen’s Disease.</p

Annual incidence of Hansen’s Disease (HD) diagnosis in Brazil, by region [6].

<p>The top graph is the total number of new cases of paucibacillary (PB) disease, while the bottom graph is the number of new cases of multibacillary (MB) disease.</p

Posterior distribution of parameters for the best model of Hansen’s Disease by region of Brazil.

<p>All results are from Model 3. The top right graph shows the transmission parameter for multibacillary cases, the top left graph shows the transmission parameter for paucibacillary cases, the bottom left graph shows the progression rate for multibacillary cases, and the bottom right graph shows the progression rate for paucibacillary cases. Each line represents a different region: North (black solid), Northeast (NE, red dashed), South (blue dots), Southeast (SE, orange dot-dash), and Midwest (MW, purple long dash).</p