Cancer is a leading cause of human death worldwide. Drug resistance, mainly caused by gene mutation, is a key obstacle to tumour treatment. Therefore, studying the mechanisms of drug resistance in cancer is extremely valuable for clinical applications.

:This paper aims to review bioinformatics approaches and mathematical models for determining the evolutionary mechanisms of drug resistance and investigating their functions in designing therapy schemes for cancer diseases. We focus on the models with drug resistance based on genetic mutations for cancer therapy and bioinformatics approaches to study drug resistance involving gene co-expression networks and machine learning algorithms.

:We first review mathematical models with single-drug resistance and multidrug resistance. The resistance probability of a drug is different from the order of drug administration in a multidrug resistance model. Then, we discuss bioinformatics methods and machine learning algorithms that are designed to develop gene co-expression networks and explore the functions of gene mutations in drug resistance using multi-omics datasets of cancer cells, which can be used to predict individual drug response and prognostic biomarkers.

:It was found that the resistance probability and expected number of drug-resistant tumour cells increase with the increase in the net reproductive rate of resistant tumour cells. Constrained models, such as logistical growth resistance models, can be used to identify more clinically realistic treatment strategies for cancer therapy. In addition, bioinformatics methods and machine learning algorithms can also lead to the development of effective therapy schemes.