Abstract
Combination therapies have shown remarkable success in preventing the evolution of resistance to multiple drugs, including HIV, tuberculosis, and cancer. Nevertheless, the rise in drug resistance still remains an important challenge. The capability to accurately predict the emergence of resistance, either to one or multiple drugs, may help to improve treatment options. Existing theoretical approaches often focus on exponential growth laws, which may not be realistic when scarce resources and competition limit growth. In this work, we study the emergence of single and double drug resistance in a model of combination therapy of two drugs. The model describes a sensitive strain, two types of single-resistant strains, and a double-resistant strain. We compare the probability that resistance emerges for three growth laws: exponential growth, logistic growth without competition between strains, and logistic growth with competition between strains. Using mathematical estimates and numerical simulations, we show that between-strain competition only affects the emergence of single resistance when resources are scarce. In contrast, the probability of double resistance is affected by between-strain competition over a wider space of resource availability. This indicates that competition between different resistant strains may be pertinent to identifying strategies for suppressing drug resistance, and that exponential models may overestimate the emergence of resistance to multiple drugs. A by-product of our work is an efficient strategy to evaluate probabilities of single and double resistance in models with multiple sequential mutations. This may be useful for a range of other problems in which the probability of resistance is of interest.
Highlights
The rise of drug resistance has triggered studies into different treatment regimes, aimed to prevent or delay the emergence of resistance
We describe the evolution of resistance by means of three stochastic models: (i) a model with no interactions between cells, leading to exponential growth if growth rates are constant; (ii) a model in which each strain follows a logistic growth law, but where there are no interactions between the different strains; (iii) logistic growth with competition between strains for a common resource
Models for estimating the probability of drug resistance have previously been largely based on exponential growth (some exceptions are Austin and Anderson (1999), Baker et al (2016))
Summary
The rise of drug resistance has triggered studies into different treatment regimes, aimed to prevent or delay the emergence of resistance. Since mutations occur as random events, one of the main aims is to compute or estimate the probability that resistant cells are present in the population at a certain time after the drug treatment has started. The purpose of this work is to show how the choice of growth model affects predictions for the emergence of single and double resistance under combination therapy. The probability of double resistance varies across the different growth models for a larger range of parameters (such as birth rates of sensitive or resistant strains, or the initial cell number). This difference to the exponential model is more pronounced in the model with competition between different strains. Further details of our calculations, and additional results can be found in the Supplementary Material
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