Eur J Clin Microbiol Infect Dis. 2016 Aug; 35:1259. doi:10.1007/s10096-016-2659-z

Modeling and predicting drug resistance rate and strength 

*Fullybright R, Dwivedi A, Mallawaarachchi  I, Sinsin B 

*Department of Applied Research, Applied-Research Center for True Development, 4016 rue Prefontaine, # 201, Montréal, Québec H1W 0A3, Canada



Drug resistance has been worsening in human infectious diseases medicine over the past several decades. Our ability to successfully control resistance depends to a large extent on our understanding of the features characterizing the process. Part of that understanding includes the rate at which new resistance has been emerging in pathogens. Along that line, resistance data covering 90 infectious diseases, 118 pathogens, and 337 molecules, from 1921 through 2007, are modeled using various statistical tools to generate regression models for the rate of new resistance emergence and for cumulative resistance build-up in pathogens. Thereafter, the strength of the association between the number of molecules put on the market and the number of resulting cases of resistance is statistically tested. Predictive models are presented for the rate at which new resistance has been emerging in infectious diseases medicine, along with predictive models for the rate of cumulative resistance build-up in the aggregate of 118 pathogens as well as in ten individual pathogens. The models are expressed as a function of time and/or as a function of the number of molecules put on the market by the pharmaceutical industry. It is found that molecules significantly induce resistance in pathogens and that new or cumulative drug resistance across infectious diseases medicine has been arising at exponential rates. 

PMID: 27209288



It’s been a long time now that drug resistance has appeared on the stage of human and veterinary medicines. Although losses are acknowledged to have been rising ever since the first case occurred about a hundred years ago, it has not been possible to track the exact rate of growth of drug resistance, especially in human infectious diseases medicine. Clinicians have long been complaining of worsening pathogen resistance to drugs and have been reporting increasing difficulty in their attempts to cure infections in hospital settings, but how fast this worsening resistance is happening has remained unknown—and so have predictions of what the trend is likely to be in the future.

We have therefore set out to make an analysis of the resistance propagation process, with the goal of developing predictive mathematical models which can inform of the rate at which new resistance has been emerging but also of the rate of growth of cumulative resistance in infectious diseases medicine taken as a whole.

However, to reach the goal of accurately predicting the rate of occurrence of these processes, it was necessary to first break drug resistance into subsets that we’ve termed resistance layers, and then to take into account the extent of the resistance on each layer, which we’ve called resistance strength. Once those foundational definitions were set, the predictive models were able to be generated and presented.




Figure 1: Cumulative Molecules & Monotherapy Resistances vs Time.  Assuming that 1 antibiotic molecule replaces 1 monotherapy resistance, the green area at the bottom indicates how many antibiotics are available to combat resistance, while the red area at the top, which overlaps the green one, shows how many resistances we are facing. For the medical community to win the resistance challenge, the green area should be greater than and overlap the red one—which is not the case. 


The importance of this study is triple:

·         First, the study tells us that the rate of new resistance emergence in infectious diseases medicine taken as a whole is very high: exponential, far higher than the pace at which we’ve been manufacturing new drugs to replace old, ineffective ones. This explains why clinicians have been facing increasing difficulty in curing resistant infections in hospital settings.

·         Second, by presenting models characterizing the rate of the resistance emergence process in pathogens, on the one hand, and the rate of the drug manufacture process by the pharmaceutial industry, on the other hand, this study makes it possible to compute, literary, whether we have any chnace of winning the fight against pathogen resistance either now or in the future. Once these computations are made, the models clearly reveal that we are not in a positon to win this fight (1). Figure 1 shows a graphical representation of Model 4 (cumulative monotherapy resistances, with time as a predictor) and Model 25 (cumulative monotherapy drugs manufactured, with time as a predictor) as reported in the study. For us to win the fight against resistance, the green area (representing Model 25) should remain above and beyond the red area (representing Model 4), for increasing values of elapsed time. However, it can be seen in the figure that the current situation is actually the opposite, where the red area is above and beyond the green one for increasing values of elasped time, meaning that we are set to be lagging behind for ever. So, we are lagging behind in terms of first-layer (monotherapy) resistances, while a similar phenomenon is occurring on the other layers as well. It can therefore be seen that the situation is really serious.

·         Third, the study, by presenting models which reveal through clear mathematical computations that the measures we have been implementing so far are failing to contain resistance (since resistance keeps rising—fast), suggests a required unraveling of that which we are currently doing toward resistance containment. In fact, the medical community has been thinking that it is the amount (‘abuse’) or ‘misuse’ of antibiotics in the human population that is responsible for the rise and strengthening of resistance in pathogens. However, it is none of those: the way the drugs are designed rather is the culprit, and drug resistance abatement will occur once rectifications are made to drug design. This understanding is expanded in another one of our papers (2).



1. Fullybright, R (2016) The slippery difficulty of ever containing drug resistance with current practices. Eur J Clin Microbiol Infect Dis. doi:10.1007/s10096-016-2855-x 

2. Fullybright, R (2017) Characterization of biological resistance and successful drug resistance control in medicine. Front Microbiol. Under review. 



Much gratitude is expressed to the French/Canadian Agence Universitaire de la Francophonie, a government agency, for making the Campus Numérique Francophone computer resources center available—thereby making this research possible.



Rudolf Fullybright, President

Applied-Research Center for True Development

4016 rue Prefontaine, # 201

Montréal, Québec H1W 0A3




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