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In this paper we consider a combination therapy of cancer. One drug is a vaccine which activates dendritic cells so that they induce more T cells to infiltrate the tumor. The other drug is a checkpoint inhibitor, which enables the T cells to remain active against the cancer cells. The two drugs are positively correlated in the sense that an increase in the amount of each drug results in a reduction in the tumor volume. We consider the question whether a treatment with combination of the two drugs at certain levels is preferable to a treatment by one of the drugs alone at 'roughly' twice the dosage level; if that is the case, then we say that there is a positive 'synergy' for this combination of dosages. To address this question, we develop a mathematical model using a system of partial differential equations. The variables include dendritic and cancer cells, CD4+ and CD8+ T cells, IL-12 and IL-2, GM-CSF produced by the vaccine, and a T cell checkpoint inhibitor associated with PD-1. We use the model to explore the efficacy of the two drugs, separately and in combination, and compare the simulations with data from mouse experiments. We next introduce the concept of synergy between the drugs and develop a synergy map which suggests in what proportion to administer the drugs in order to achieve the maximum reduction of tumor volume under the constraint of maximum tolerated dose.

Oncolytic virus (OV) is a replication competent virus that selectively invades cancer cells; as these cells die under the viral burden, the released virus particles proceed to infect other cancer cells. Oncolytic viruses are designed to also be able to stimulate the anticancer immune response. Thus, one may represent an OV by two parameters: its replication potential and its immunogenicity. In this paper we consider a combination therapy with OV and a checkpoint inhibitor, anti-PD-1. We evaluate the efficacy of the combination therapy in terms of the tumor volume at some later time, for example, 6 months from initial treatment. Since T cells kill not only virus-free cancer cells but also virus-infected cancer cells, the following question arises: Does increasing the amount of the checkpoint inhibitor always improve the efficacy? We address this question, by a mathematical model consisting of a system of partial differential equations. We use the model to construct, by simulations, an efficacy map in terms of the doses of the checkpoint inhibitor and the OV injection. We show that there are regions in the map where an increase in the checkpoint inhibitor actually decreases the efficacy of the treatment. We also construct efficacy maps with checkpoint inhibitor vs. the replication potential of the virus that show the same antagonism, namely, an increase in the checkpoint inhibitor may actually decrease the efficacy. These results have implications for clinical trials.

Lung cancer, primarily non-small-cell lung cancer (NSCLC), is the leading cause of cancer deaths in the United States and worldwide. While early detection significantly improves five-year survival, there are no reliable diagnostic tools for early detection. Several exosomal microRNAs (miRs) are overexpressed in NSCLC, and have been suggested as potential biomarkers for early detection. The present paper develops a mathematical model for early stage of NSCLC with emphasis on the role of the three highest overexpressed miRs, namely miR-21, miR-205 and miR-155. Simulations of the model provide quantitative relationships between the tumor volume and the total mass of each of the above miRs in the tumor. Because of the positive correlation between these miRs in the tumor tissue and in the blood, the results of the paper may be viewed as a first step toward establishing a combination of miRs 21, 205, 155 and possibly other miRs as serum biomarkers for early detection of NSCLC.

Drug resistance is a primary obstacle in cancer treatment. In many patients who at first respond well to treatment, relapse occurs later on. Various mechanisms have been explored to explain drug resistance in specific cancers and for specific drugs. In this paper, we consider resistance to anti-PD-1, a drug that enhances the activity of anti-cancer T cells. Based on results in experimental melanoma, it is shown, by a mathematical model, that resistances to anti-PD-1 can be significantly reduced by combining it with anti-TNF-α. The model is used to simulate the efficacy of the combined therapy with different range of doses, different initial tumor volume, and different schedules. In particular, it is shown that under a course of treatment with 3-week cycles where each drug is injected in the first day of either week 1 or week 2, injecting anti-TNF-α one week after anti-PD-1 is the most effective schedule in reducing tumor volume.

In this paper, the repulsion effect of superinfecting virion by infected cells is studied by a reaction diffusion equation model for virus infection dynamics. In this model, the diffusion of virus depends not only on its concentration gradient but also on the concentration of infected cells. The basic reproduction number, linear stability of steady states, spreading speed and existence of traveling wave solutions for the model are discussed. It is shown that viruses spread more rapidly with the repulsion effect of infected cells on superinfecting virions, than with random diffusion only. For our model, the spreading speed of free virus is not consistent with the minimal traveling wave speed. With our general model, numerical computations of the spreading speed show that the repulsion of superinfecting virion promotes the spread of virus, which confirms, not only qualitatively but also quantitatively, the experimental result of Doceul et al. (Science 327:873–876, 2010 ).

To control the HIV/AIDS epidemics in Guangxi Zhuang Autonomous Region in China, Guangxi government launched the 5-year Guangxi AIDS Conquering Project (GACP, Phase I: 2010-2014, Phase II: 2015-2020). In the project, three measures are implemented, such as great improvements of the coverage of HIV/AIDS education, promotion of HIV voluntary counseling and testing, and enhancement of antiretroviral treatment. In this paper, we explore the effects of the three measures of GACP by construction of a Susceptible-Infected-Diagnosed-Treated population compartments model and via evaluation of the basic reproduction number derived from the model. A computational framework is developed for estimating the model parameters based on the HIV surveillance data, with application of the Markov-Chain Monte-Carlo method and Nonlinear Least Squares method. By estimating the new infections and evaluating the basic reproduction number, we find that the implementation of the three measures of GACP has a significant effect on controlling the rise of HIV/AIDS cases and the epidemic trend. Compared with HIV voluntary counseling and testing, strengthening HIV/AIDS education and expanding the coverage of antiretroviral treatment show a greater impact on HIV/AIDS epidemic control, which provides a reference project for other provinces with a similar epidemic situation in Guangxi Zhuang Autonomous Region. At the same time, our research fills the current research gap for the evaluation of large-scale AIDS prevention and control projects in developing areas.

Skeletal muscle satellite cells (SMSCs), also known as a multipotential stem cell population, play a crucial role during muscle growth and regeneration. In recent years, numerous miRNAs have been associated with the proliferation and differentiation of SMSCs in a number of mammalian species; however, the regulatory mechanisms of miR-194-5p in rabbit SMSCs still remain scarce. In this study, miR-194-5p was first observed to be highly expressed in the rabbit leg muscle. Furthermore, both the mimics and inhibitor of miR-194-5p were used to explore its role in the proliferation and differentiation of rabbit SMSCs cultured in vitro. Results from both EdU and CCK8 assays showed that miR-194-5p inhibited the proliferation of SMSCs. Meanwhile, Mef2c was identified as a target gene of miR-194-5p based on the dual-luciferase reporter assay results. In addition, upregulation of miR-194-5p decreased the expression levels of Mef2c and MyoG during rabbit SMSCs differentiation on Days 3 and 7 of in vitro culture. Taken together, these data demonstrated that miR-194-5p negatively regulates the proliferation and differentiation of rabbit SMSCs by targeting Mef2c.

Patients with chronic myeloid leukemia (CML) who receive tyrosine kinase inhibitors (TKIs) have been known to achieve treatment-free remission (TFR) upon discontinuing treatment. However, the underlying mechanisms of this phenomenon remain incompletely understood. This study aims to elucidate the mechanism of TFR in CML patients, focusing on the feedback interaction between leukemia stem cells and the bone marrow microenvironment. We have developed a mathematical model to explore the interplay between leukemia stem cells and the bone marrow microenvironment, allowing for the simulation of CML progression dynamics. Our proposed model reveals a dichotomous response following TKI discontinuation, with two distinct patient groups emerging: one prone to early molecular relapse and the other capable of achieving long-term TFR after treatment cessation. This finding aligns with clinical observations and underscores the essential role of feedback interaction between leukemic cells and the tumor microenvironment in sustaining TFR. Notably, we have shown that the ratio of leukemia cells in peripheral blood (PBLC) and the tumor microenvironment (TME) index can be a valuable predictive tool for identifying patients likely to achieve TFR after discontinuing treatment. This study provides fresh insights into the mechanism of TFR in CML patients and underscores the significance of microenvironmental control in achieving TFR.

Endoplasmic reticulum (ER) stress is implicated in the pathogenesis of many diseases, including myocardial ischemia/reperfusion injury. We hypothesized that human umbilical cord mesenchymal stromal cells derived extracellular vesicles (HuMSC-EVs) could protect cardiac cells against hyperactive ER stress induced by hypoxia/reoxygenation (H/R) injury. The H/R model was generated using the H9c2 cultured cardiac cell line. HuMSC-EVs were extracted using a commercially available exosome isolation reagent. Levels of apoptosis-related signaling molecules and the degree of ER stress were assessed by western blot. The role of the PI3K/Akt pathway was investigated using signaling inhibitors. Lactate dehydrogenase leakage and 3-(4,5-Dimethylthiazol-2-yl)-2,5-Diphenyltetrazolium Bromide (MTT) analysis were used for evaluating the therapeutic effects of HuMSC-EVs in vitro. The results showed that ER stress and the rate of apoptosis were increased in the context of H/R injury. Treatment with HuMSC-EVs inhibited ER stress and increased survival in H9c2 cells exposed to H/R. Mechanistically, the PI3K/Akt pathway was activated by treatment with HuMSC-EVs after H/R. Inhibition of the PI3K/Akt pathway by a specific inhibitor, LY294002, partially reduced the protective effect of HuMSC-EVs. Our findings suggest that HuMSC-EVs could alleviate ER stress–induced apoptosis during H/R via activation of the PI3K/Akt pathway.

Recently, it has been proved that for the diffusive viral infection model with cell-to-cell infection, the virus-free steady state is globally attractive when the basic reproduction number < 1, and the virus is uniformly persistent if > 1. However, the global stability analysis in the critical case of = 1 is not given due to a technical difficulty. For the diffusive viral infection model including a single equation with diffusion term, global stability analysis in the critical case has been performed by constructing Lyapunov functions. Unfortunately, this method is not applicable for two or more equations with diffusion terms, which was left it as an open problem. The present study is devoted to solving this open problem and shows that is globally asymptotically stable when = 1 for three equations with diffusion terms by means of Gronwall's inequality, comparison theorem and the properties of semigroup.