This study investigates the influence of fear, refuge, and migration in a predator–prey model, where the interactions between the species follow an asymmetric function response. In contrast to some other findings, we propose that prey develop an anti-predator response in response to a concentration of predators, which in turn increases the fear factor of the predators. The conditions under which all ecologically meaningful equilibrium points exist are discussed in detail. The local and global dynamics of the model are determined at all equilibrium points. The model admits several interesting results by changing the rate of fear of predators and predator aggregate sensitivity. Numerical simulations have been performed to verify our theoret

Taking into account the significance of food chains in the environment, it demonstrates the interdependence of all living things and has economic implications for people. Hunting cooperation, fear, and intraspecific competition are all included in a food chain model that has been developed and researched. The study tries to comprehend how these elements affect the behavior of species along the food chain. We first examined the suggested model's solution properties before calculating every potential equilibrium point and examining the stability and bifurcation nearby. We have identified the factors that guarantee the global stability of the positive equilibrium point using the geometric approach. Additionally, the circumstances that would gu

In this work, a numerical study is performed to predict the solution of two – dimensional, steady and laminar mixed convection flow over a square cylinder placed symmetrically in a vertical parallel plate. A finite difference method is employed to solve the governing differential equations, continuity, momentum, and energy equation balances. The solution is obtained for stream function, vorticity and temperature as dependent variables by iterative technique known as successive over relaxation. The flow and temperature patterns are obtained for Reynolds number and Grashof number at (Re= -50,50,100,-100) (positive or negative value refers to aidding or opposing buoyancy , +1 assisting flow, -1 opposing flow) and (102 to 105) , respective

Purpose: To explore whether baseline matrix metalloproteinase (MMP)-8 level in gingival crevicular fluid (GCF) (exposure) can predict the outcome (reduction in probing pocket depth (PPD) (outcome)) of nonsurgical periodontal therapy (NSPT) (manual or ultrasonic or both) in patients with periodontitis (population/problem) after 3 months. Methods: Six databases (PubMed, Cochrane library, ProQuest, Ovid, Scopus, EBSCO) were searched for relevant articles published until 30 July 2021. Retrieved articles were passed through a three-phase filtration process on the basis of the eligibility criteria. The primary outcome was the change in PPD after 3 months. Quality of the selected articles was assessed using Cochrane Risk of Bias tool (RoB2

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami