Stability of solution of Kuramoto-Sivashinsky-Korteweg-de Vries system

Abstract-A model consisting of a mixed Kuramoto-Sivashinsky-Korteweg-de Vries equation, linearly coupled to an extra linear dissipative equation has been proposed in [1] in order to describe the surface waves on multilayered liquid films and stability criteria are discussed using wave mode analysis. In this paper, we study the linear stability of solutions to the model from the viewpoint of energy estimate

A mathematical model for predicting and controlling COVID-19 transmission with impulsive vaccination

This study examines an epidemiological model known as the susceptible-exposed-infected-hospitalized-recovered (SEIHR) model, with and without impulsive vaccination strategies. First, the model was analyzed without impulsive vaccination in the presence of a reinfection effect. Subsequently, it was studied as part of a periodic impulsive vaccination strategy targeting the susceptible population. These vaccination impulses were administered in very brief intervals at specific time instants, with a fixed time gap between each impulse. The two approaches can be modified to respond to different amounts of susceptibility, with control efforts intensifying as susceptibility levels rise. The model's analysis includes crucial aspects such as the non-negativity of solutions, the existence of steady states, and the stability corresponding to the basic reproduction number. We demonstrate that when vaccination measures are taken into account, the basic reproduction number remains as less than one. Therefore, the disease-free equilibrium in the case of vaccination could still be asymptotically stable at the higher disease transmission rate, as compared to the case of no vaccination in which the disease-free equilibrium may no longer be asymptotically stable. Furthermore, we show that when the disease-free equilibrium is stable, the endemic equilibrium cannot be attained, and that when the reproduction number rises above unity, the disease-free equilibrium becomes unstable while the endemic equilibrium becomes stable. We have also derived conditions for the global stability of both equilibriums. To support our theoretical results, we have constructed a time series of numerical simulations and compared them with real-world data from the ongoing SARS-CoV-2 (COVID-19) pandemic

Materials in particulate form for tissue engineering. 2 Applications in bone

Materials in particulate form have been the subjects of intensive research in view of their use as drug delivery systems. While within this application there are still issues to be addressed, these systems are now being regarded as having a great potential for tissue engineering applications. Bone repair is a very demanding task, due to the specific characteristics of skeletal tissues, and the design of scaffolds for bone tissue engineering presents several difficulties. Materials in particulate form are now seen as a means of achieving higher control over parameters such as porosity, pore size, surface area and the mechanical properties of the scaffold. These materials also have the potential to incorporate biologically active molecules for release and to serve as carriers for cells. It is believed that the combination of these features would create a more efficient approach towards regeneration. This review focuses on the application ofmaterials in particulate formfor bone tissue engineering. A brief overview of bone biology and the healing process is also provided in order to place the application in its broader context. An original compilation of molecules with a documented role in bone tissue biology is listed, as they have the potential to be used in bone tissue engineering strategies. To sum up this review, examples of works addressing the above aspects are presented

An impulsive mathematical model of bone formation and resorption: effects of parathyroid hormone, calcitonin and impulsive estrogen supplement

Abstract In this paper, we propose an impulsive mathematical model of bone formation and resorption accounting for the number of active osteoclastic cells, bone resorbing cells, and the number of active osteoblastic cells, bone forming cells, based on the effects of parathyroid hormone and calcitonin with impulsive estrogen supplement. The model is then analyzed theoretically in terms of its stability, permanence and oscillatory behavior. The conditions on the model parameters, for which the desirable behaviors of the solution of the system can be expected, are derived. Numerical simulations are also carried out in order to support our theoretical predictions. The results indicate that the frequency and dosage of the estrogen supplements are important since the behavior of the solution of the system depends on the frequency and dosage of the estrogen supplements

Effect of increased global temperatures on biological control of green lacewings on the spread of mealybugs in a cassava field: a simulation study

Abstract Even though the effect of release frequency of green lacewings in controlling the spread of mealybugs in a cassava field was investigated by Promrak and Rattanakul in 2015, the effect of increased global temperature was not taken into account. In this work, cellular automata and Monte Carlo simulation are employed in order to study the effect of an increased global temperature on the life cycles of mealybugs and green lacewings which in turn effects the efficacy of the biological control of the spread of mealybugs. Computer simulations are carried out at different temperatures so that an efficient biological control of the spread of mealybugs in a cassava field is obtained

Modeling calcium signaling by Cellular Automata simulation incorporating endocrine regulation and trafficking in various types of receptors

Abstract Calcium signaling plays important physiological roles which range widely from activation of muscle, synaptic transmission, cell movement, fertilization, growth in the cell population, learning process and retention of memory, to saliva secretion. Calcium also plays a crucial role in biochemical processes such as enzyme activity regulation, ion channels permeability, including activity of ion pumps, and different parts of the cytoskeleton. Signaling is initiated when the cell is stimulated, which results in the release of calcium ions (Ca2+) from intracellular stores. Many cell surface receptors, including G protein-coupled receptors, stimulate the formation of IP3 that diffuses to the endoplasmic reticulum, binds to its receptor, leading to the release of Ca2+ from the endoplasmic reticulum. Here, we construct a Cellular Automata model of signal transduction pathway mediated by calcium sensing receptors. The mechanism of receptor trafficking and dimerization is taken into account to exert positive feedback effects on the binding affinity of the cognate receptors. Difference equations are utilized to update the levels of calcium in the intracellular and extracellular compartments, incorporating endocrine regulation through the parathyroid hormone. Time series of calcium concentrations are obtained to investigate the effects of different fractions of healthy (functional) and defective receptors as well as dimerization process