In this paper, an SEIR epidemic model for an imperfect treatment disease with age-dependent latency and relapse is proposed. The model is well-suited to model tuberculosis. The basic reproduction number R0 is calculated. We obtain the global behavior of the model in terms of R0. If R0< 1, the disease-free equilibrium is globally asymptotically stable, whereas if R0>1, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present.

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Background: 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. Objective: 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. Results: 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. Conclusion: 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.

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In the first wave of the COVID-19 outbreak in China, the epidemic has spread rapidly due to interprovincial migration from Wuhan to Hubei province and to the rest of China. Based on Chinas interprovincial migration and outbreak data, this paper established panel models. The transmission of the first wave of COVID-19 of China can be divided into two stages: a phase of national outbreak caused by interprovincial migration and a phase of sustained development due to close contacts. Interprovincial migration triggered a nationwide outbreak that lasted until around 28 January 2020, about 5 days after the Wuhan lockdown. In this phase of transmission, the population inflow from Hubei province was more contagious than the inflow from other provinces. The results also show that the sum of the influence coefficients of interprovincial population inflow is less than 1, which means a state of convergence, indicating that “Wuhan lockdown” is an effective measure to cut off the spread of the epidemic by interprovincial migration.