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.

It has previously been shown that the rate of drug resistance emergence in medicine is exponential, while we have been producing drugs at a much lower rate. Our ability to successfully contain resistance at any one time is function of how many drugs we have at our disposal to counter new resistances from pathogens. Here, we assess our level of preparedness through a mathematical comparison of the drug manufacture rate by the pharmaceutical industry with the resistance emergence rate in pathogens. To that effect, changes in the rates of growth of the drugs production and resistance emergence processes are computed over multiple time segments and compared. It is found that new resistance emergence rate in infectious diseases medicine remains mathematically and permanently ahead of the drugs production rate by the pharmaceutical industry. Consequently, we are not in a position to ever contain current or future strengths of resistance from pathogens. A review of current practices is called for.

It has now been a century that drug resistance has been getting worse in human infectious diseases medicine. A similar trend is observed in veterinary medicine and agriculture. The successful control of drug resistance requires an understanding of biological resistance in general, as a phenomenon taking place in nature. Once we have understood the main characteristics of biological resistance and how it operates in nature, we can then apply that new understanding to its subset that drug resistance in human medicine is. Possession of such an edge can also lead to the successful control of resistance in veterinary medicine, in agriculture, and in other settings of resistance activity by biological organisms. Based on biological resistance data from human medicine, veterinary medicine, and agriculture, some of the fundamental characteristics of resistance as a natural process displayed by all living organisms are established. The consistent, common features characterizing the data are exploited, as is a mathematical model depicting how biological resistance strengthens in living organisms. It is found that biological resistance in general, and drug resistance in particular, is a phenomenon governed by at least two laws: the First Law of Resistance, requiring a threshold to be met before resistance can be prevented and the Second Law of Resistance, causing resistance to strengthen to infinite levels if unstopped. Inference is thereafter made as to the drug design strategy required for the successful control of resistance in medicine. To that end, the blueprint currently applied in the design of infectious diseases drugs needs revising.

In a companion article, we have shown that Einstein's special principle of relativity holds more potential than has so far been understood. The ability of the principle to translate physical laws allows our faster understanding and control of physical reality. Derivation of the Third Law of Resistance, towards the successful control of biological organisms, is an example of such faster understanding and control of a physical phenomenon. Resistance in medicine has been worsening for 100 years now, and this phenomenon has eluded every control measure since, while resistance in agriculture displays similarly aggravating trends, both coming with serious economic and human life losses. Earlier analysis of resistance in the biological realm has shown that the process is governed by at least two laws: the First Law of Resistance conditioning its rise and the Second Law of Resistance conditioning its growth. Here, moving on from the interpreted Einstein’s special principle of relativity and the modified Newton's Third Law of Motion, we show that resistance is governed by a Third Law which conditions its termination. Application of the Third Law of Resistance to pathogens points to the immediate steps we need to take towards the successful control of resistance in medicine and agriculture.

10Accurate quantification of biological resistance has been impossible so far. Among the various forms of biological resistance which exist in nature, pathogen resistance to drugs is a familiar one.However, as in the case of other forms of resistance, accurately quantifying drug resistance in pathogens has been impossible up to now. Here, we introduce a mathematically-defined and uniform procedure for the absolute quantification of biological resistance deployed by any living organism in 15 the biological realm, including and beyond drug resistance in medicine. The scheme introduced makes possible the exact measurement or computation of the extent to which resistance is deployed by any living organism regardless of kingdom and regardless of the mechanism of resistance involved.Furthermore, the Second Law of Resistance indicating that resistance has the potential to increase to infinite levels, and the Third Law of Resistance indicating that resistance comes to an end once 20 interaction stops, the resistance unit function introduced here is fully compatible with both the Second and Third Laws of Resistance. 25Keywords: pathogen; antibiotic; antimicrobial; drug; resistance; biological; organism; law; unit; scale. Significance Statement 30Biological resistance is a phenomenon displayed by all living organisms, from the microscopic to the macroscopic. However, it takes place through a wide array of mechanisms and can be deployed to any strengths. These features make exact quantification of biological resistance impossible. It has so far been impossible to quantify resistance absolutely. Here, we introduce a radioactivity decay process categorization of biological resistance and derive a mathematical expression allowing the absolute