Modelling and Analysis of a Holling Type II Stage Structured Predator-Prey System in the Presence of Harvesting

The effect of harvesting and predation on a Holling type II stage-structured predator-prey system with assumption that harvesting and predation happen only to mature preys was investigated. Stability of interior point was analysed using Routh Hurwith Criterion. Numerical simulations were carried out. The results show that harvesting and predation have strong negative impacts on population dynamics of stage structured predator-prey system.Keywords: Predator-prey System; Stage Structure; Holling type II; Harvestin

Effects of magnetic fields on an unsteady mixed convective boundary layer flow of an electrically conducting fluid with temperature dependent properties

A mixed convective boundary layer flow of an electrically conducting fluid with temperature dependent properties over an inclined plate is investigated. The magnetohydrodynamic boundary layer governing equations are derived by using Boussinesq and boundary layer approximations. The equations are transformed to similarity form using a similarity transformation variable and the resulting boundary value problem is solved numerically. The effects of magnetic fields, unsteadiness, mixed convection and variable fluid properties on velocity and temperature in the boundary layer are analysed. The effects of pertinent parameters on skin friction and heat transfer are also analysed.Keywords: Magnetohydrodynamics; Mixed convection; Boundary layer; Temperature dependent fluid properties.

1-D Transport Behaviour of Emerging Contaminants in the Unidirectional Flowing Surface Waters of the Msimbazi River

The primary objectives of this investigation of environmental pollution were to assess spatio-temporal concentrations and predictions of transport behaviour of pollutants in aqueous media. In order to attain these goals for the Msimbazi river, the analytical and numerical solutions to the 1-D advection-dispersion equation (ADE) implemented the first-type inlet condition. The MATLAB software was used to solve the analytical equation resulting from the ADE equation. The solution to the ADE model enabled effective prediction of contaminants’spatial distribution within a distance of 200 m from a point source in the direction of flowing water. Among the first and third-types inlet conditions, the first-type had the best exponential concentration prediction with descending concentration gradients between –100 ng/L.m and –0.4 ng/L.m, while beyond it the concentration gradient was merely constant. These findings are the first of this type in our region to the best of our knowledge, and hence a milestone for understanding the transport behaviour of emerging contaminants, and enable estimation of probable pollution-free zones. This study gave results that can form a basis for analytical and public interventions. Keywords: Modelling emerging contaminants; Advection-Dispersion Equation; Contaminants transport; First-type inlet condition; Concentration gradien

Szegő's problem on curves

<p>(a) Map of Kenya showing HIV prevalence distributions. The color bar from blue to red is in the order of increasing HIV prevalence. For clarity, the names of counties included are the only ones included in this study (Source of data:ArcGIS.com: shapefile-The 47 counties of Kenya (shapefile by dmuthami <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142805#pone.0142805.s005" target="_blank">S5 Table</a>) and HIV data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142805#pone.0142805.ref039" target="_blank">39</a>]. (b) Human travel networks (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142805#pone.0142805.s006" target="_blank">S6 Table</a>) as estimated by [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142805#pone.0142805.ref038" target="_blank">38</a>]. Monthly average number of trips per 1000 individuals between all pairs of regions over the course of the year. For clarity, only trips made per 1000 individuals that are more than 60 trips per year are shown, with arrows indicating the direction of movements from home region to a visited region. The thickness of the arrow represents the number of trips made.</p

The Use of Non-Standard Finite Difference Schemes to Solve the DAMP and SIT Models

Abstract Sterile insect technique (SIT) is a method of biological control that uses sterile male insects to reduce the reproductive rate of a species of target insect. The method relies on the release of sterile or treated males in order to reduce the native population of insects. We propose the model that governs the dynamics of the anopheles mosquito population, and then modify to incorporate the sterile insect technique as an intervention to curtail the reproduction of mosquitoes. The nonstandard finite difference numerical schemes and simulations for these models are provided. The results indicate that sterile technique with frequent and high rate of release can be an alternative to chemical control tools in the fight against malaria

MHD Arterial Blood Flow and Mass Transfer under the Presence of Stenosis, Body Acceleration and Chemical Reaction: A Case of Magnetic Therapy

This research article published by the Journal of Mathematics and Informatics, 2020A mathematical model has been developed and used to study pulsatile blood flow and mass transfer through a stenosed artery in the presence of body acceleration and magnetic fields. An explicit Finite Difference Method (FDM) has been used to discretize the formulated mathematical model. The discretized model equations were solved in MATLAB software to produce simulations. The effect of Hartman number, Reynolds number, Schmidt number, stenotic height, body acceleration and chemical reactions have been investigated. It has been observed that, the velocity, concentration and skin friction, decrease with increasing stenotic height. Velocity on the other hand increases, as body acceleration increases. It has further been observed that as the Hartman number increases, both the radial and axial velocities diminish. Increase of the Reynolds number results in the increase of the velocity profiles. The higher the chemical reaction parameter is, the lower are the concentration profiles

Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model

When both human and mosquito populations vary, forward bifurcation occurs if the basic reproduction number R0 is less than one in the absence of disease-induced death. When the disease-induced death rate is large enough R0 = 1 is a subcritical backward bifurcation point. The domain for the study of the dynamics is reduced to a compact and feasible region, where the system admits a speci c algebraic decomposition into infective and non-infected humans and mosquitoes. Stability results are extended and the possibility of backward bifurcation is clari ed. A dynamically consistent nonstandard nite di erence scheme is designed.Yves Dumont was supported jointly by the French Ministry of Health and the 2007–2013 Convergence program of the European Regional Development Fund (ERDF). Roumen Anguelov, Jean Lubuma, and Eunice Mureithi thank the South African National Research Foundation for its support.http://www.tandfonline.com/loi/gmps20hb201

An investigation on the Monkeypox virus dynamics in human and rodent populations for a deterministic mathematical model

A mathematical deterministic model for the dynamics of Monkeypox disease is developed. Monkeypox is a viral zoonotic disease that can be transmitted to humans, through contact with infected rodents. The model captures both the human and rodent populations and incorporates control strategies such as vaccines and quarantine for the human population. The model is analysed for local and global stability of the equilibrium solutions. In addition, numerical simulations of the model equations and sensitivity analysis of the parameters are carried out. The solutions obtained show that an increase in vaccination and quarantine measures could reduce the number of reproductions and ultimately eradicate the virus