In comparison with lymphomas and leukemias, chemotherapy of solid neoplasms, i.e., cancer, has much more limited success in curing the patient. This lack of efficacy of chemotherapy has been attributed to increased interstitial fluid pressure within cancers, which obstructs convection and only permits diffusion of oxygen and nutrients about 100 μm from blood vessels. As diffusion is limited to this distance, hypoxic and necrotic fractions within the tumor are observed beyond this region. The comparably small number of cancer cells that can be targeted with drugs inevitably leads to an ineffective treatment response. This study presents an analysis of the influence of interstitial fluid pressure on the chemotherapeutic effect in an HT29 human colon cancer xenograft mouse tumor model. To investigate the limited distribution of drugs into primary tumor and metastases, we developed a mathematical model describing tumor growth dynamics of oxygenated, hypoxic, and necrotic fractions, combined with a pharmacokinetic-pharmacodynamic model describing the behavior and effectivity of the chemotherapeutic agent. According to the numerical simulations, the age of the tumor at treatment was the decisive factor in the reduction in size of the primary tumor. This effect is mediated by the rapid decrease in the percentage of oxygenated cells within the tumor, which reduces the fraction of cells that can be affected by the drug. As in the primary tumor, interstitial fluid pressure builds up in metastases when they reach a specific size, leading to the formation of tumor fractions.  https://www.selleckchem.com/products/bp-1-102.html  This behavior is absent if the metastasis enters a dormant phase before the threshold for the development of interstitial fluid pressure has been reached. The small size of these metastases maximizes therapeutic success since they consist only of oxygenated cells, and the drug therefore affects all the cells.In this paper, with the assumption that infectious individuals, once recovered for a period of fixed length, will relapse back to the infectious class, we derive an epidemic model for a population living in a two-patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay accounting for the fixed constant relapse time and a non-local term caused by the mobility of the individuals during the recovered period. We explore the dynamics of the model under two scenarios (i) assuming irreducibility for three travel rate matrices; (ii) allowing reducibility in some of the three matrices. For (i), we establish the global threshold dynamics in terms of the principal eigenvalue of a 2×2 matrix. For (ii), we consider three special cases so that we can obtain some explicit results, which allow us to explicitly explore the impact of the travel rates. We find that the role that the travel rate of recovered and infectious individuals differs from that of susceptible individuals. There is also an important difference between case (i) and (ii) under (ii), a boundary equilibrium is possible while under (i) it is impossible.The whole world is devastated by the impact of the COVID-19 pandemic. The socioeconomic and other effects of COVID-19 on people are visible in all echelons of society. The main goal of countries is to stop the spreading of this pandemic by reducing the COVID-19 related new cases and deaths. In this paper, we analyzed the correlated count outcomes, daily new cases, and fatalities, and assessed the impact of some covariates by adopting a generalized bivariate Poisson model. There are different effects of duration on new cases and deaths in different countries. Also, the regional variation found to be different, and population density has a significant impact on outcomes.In this paper, a new consumer-resource competition model with a state-dependent maturity delay is developed, which incorporates one resource species and two stage-structured consumer species. The main innovation is that the model directly manifests the relationship between resources and maturity time of consumers through a correction term, $1-\tau'(x(t))x'(t)$. Firstly, the well-posedness of the solution is studied. At the same time, the existence and uniqueness of all equilibria are discussed. Then, the linearized stabilities of the equilibria are achieved. Finally, some sufficient conditions which ensure the global attractivity of the coexistence equilibrium are obtained.Soft rough set model represents a different mathematical model to which many real-life data can be connected. In fact, this theory represents a link between soft set and rough set theories. The main goal of the present paper is to introduce a new approach to modify and generalize soft rough sets. We are discussing and exploring the basic properties for these approaches. In addition, we use the suggested approaches as a mathematical modeling for an uncertain data and deal with the ambiguity. Comparisons among the proposed methods and the previous one are obtained. Finally, a medical application of the suggested approximations in decision making of diagnosis of COVID-19 is illustrated. Moreover, we develop an algorithm following these concepts and apply it to a decision making problem to demonstrate the applicability of the proposed methods.In this paper we propose a variant of a consensus-based global optimization (CBO) method that uses personal best information in order to compute the global minimum of a non-convex, locally Lipschitz continuous function. The proposed approach is motivated by the original particle swarming algorithms, in which particles adjust their position with respect to the personal best, the current global best, and some additive noise. The personal best information along an individual trajectory is included with the help of a weighted mean. This weighted mean can be computed very efficiently due to its ac-cumulative structure. It enters the dynamics via an additional drift term. We illustrate the performance with a toy example, analyze the respective memory-dependent stochastic system and compare the per-formance with the original CBO with component-wise noise for several benchmark problems. The proposed method has a higher success rate for computational experiments with a small particle number and where the initial particle distribution is disadvantageous with respect to the global minimum.