Evolutionary game theory (EGT) analyzes the stability of competing strategies for withstanding selective pressures within a population over generations. Under rapid shifts in selective pressures (e
According to the Target Theory, the tumor population is divided into multiple different subpopulations, called targets, based on the diverse effects of ionizing radiation on human cells. Radiation particles can cause single or double-strand break(s). As such, cells are divided into three subpopulations, namely cells with no DNA fragmentation, cells with DNA single-strand breaks, and cells with DNA double-strand breaks. This work introduces a hybrid differential equation model, with coefficients described by random variables representing transition rates between targets. The model is utilized to simulate the dynamics of targets and describes the cell damage heterogeneity and the repair mechanism between two consecutive dose fractions. Therefore, a new definition of tumor lifespan based on population size is achieved. Stability and bifurcation analysis are performed. Finally, the probability of target inactivity after radiation and the probability of target re-activation following the repair mechanism are evaluated with respect to the tumor lifespan.
Liver cirrhosis and hepatocellular carcinoma disease caused by the Hepatitis C virus (HCV) infection. Inside this article, a deterministic model has been formulated and analyzed for the transmission of HCV in the liver cells. We have also considered two types of viral strain (wild and mutant). We have also projected a mathematical model of the effect of Sofosbuvir (SOF) together with Velpatasvir (VEL) antiviral therapy in HCV infected patients. Our analytical and numerical findings reveal that the optimal schedule of treatment for the best result should be obtained by choosing the best strategy depending on the circumstances.
Contact tracing can be an effective measure to control emerging infectious diseases, but the efficacy of contact tracing measures can depend upon the willingness of individuals to get be tested even when they are symptomatic. In this paper, we examine the effects of symptomatic individuals getting tested and the use of contact tracing in a network model of disease transmission. We utilize a network model to resolve the influence of contact patterns between individuals as apposed to assuming mass action where all individuals are connected to each other. We find that the effects of self-reporting and contact tracing vary depending on the structure of the network. We also compare the results from the network model with an analogous ODE model that assumes mass action and demonstrate how the results can be dramatically different.
It is known that in oxygen concentration profiles for capillary beds of skeletal muscles, radial diffusion most likely has considerably more effect on oxygen transport in long and parallel capillary beds than axial diffusion. However, axial diffusion may still play a significant role in oxygen transport in tissue, especially in relatively short pathways. Our model adds to known solutions the component of axial diffusion to multi-capillary beds inside a tissue cylinder, where arbitrary characteristics include random locations and uneven oxygen strengths. Discussion of the solutions for oxygen supply in multicapillary beds near the arterial ends, in the central regions, and near the venous ends in capillaries is introduced in the remainder of the article. Our prime model builds on known solutions involving circular regions by adding a $Z$-axis and by accounting for circular cylindrical tissue around multiple capillaries. To account for relatively small longitudinal diffusivities, we use perturbation methods to solve the associated governing equations.
