Peeyush Chandra

A model for fishery resource with reserve area

In this paper, we propose and analyse a mathematical model to study the dynamics of a fishery resource system in an aquatic environment that consists of two zones: a free fishing zone and a reserve zone where fishing is strictly prohibited. Biological and bionomic equilibria of the system are obtained, and criteria for local stability, instability and global stability of the system are derived. It is shown that even if fishery is exploited continuously in the unreserved zone, fish populations can be maintained at an appropriate equilibrium level in the habitat. An optimal harvesting policy is also discussed using the Pantryagins Maximum Principle.

ON THE INFLUENCE OF WALL PROPERTIES IN THE PERISTALTIC MOTION OF MICROPOLAR FLUID

We carry out a study of the peristaltic motion of an incompressible micropolar fluid in a two-dimensional channel. The effects of viscoelastic wall properties and micropolar fluid parameters on the flow are investigated using the equations of the fluid as well as of the deformable boundaries. A perturbation technique is used to determine flow characteristics. The velocity profile is presented and discussed briefly. We find the critical values of the parameters involving wall characteristics, which cause mean flow reversal.

Modeling and analysis of the algal bloom in a lake caused by discharge of nutrients

In this paper, a nonlinear model for the algal bloom in a lake caused by excessive flow of nutrients from domestic drainage and water runoff from agricultural fields, is proposed and analyzed. This model considers interactions of cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen in the lake. It is assumed that detritus, which is formed due to death of algae, supplements the cumulative concentration of the nutrients in the water body, using dissolved oxygen in the process. It is shown that the equilibrium level of algal population is highly dependent on the cumulative rate of discharge of inputs of nutrients in the lake and as this cumulative discharge increases the equilibrium level of algal population increases leading to eutrophication. It is also shown that the equilibrium level of dissolved oxygen decreases but that of detritus increases, as the rate of input of cumulative discharge increases. The same results are also found by numerical solution of the model.

A RESOURCE DEPENDENT FISHERY MODEL WITH OPTIMAL HARVESTING POLICY

A dynamic model for a single-species fishery, which depends partially on a logistically growing resource with functional response, is proposed using taxation as control instrument to protect fish population from overexploitation. The analysis of the model shows that both the equilibrium density of fish population as well as the maximum sustainable yield increase as resource biomass density increases. The optimal harvesting policy is also discussed with the help of Pontryagins Maximum Principle. It is found that for the optimum equilibrium value of resource biomass density, the total users cost of harvest per unit effort must be equal to the discounted value of future price at the steady state.

Flow of Eringen fluid (simple microfluid) through an artery with mild stenosis

This paper presents an analysis for blood flow through a stenosed artery considering the localized effects of the stenosis. The blood vessel is modelled as a rigid tube and the particulate nature of blood is accounted through an Eringen fluid (simple microfluid) model. Further a peripheral layer of Newtonian fluid has been considered in the model to account for the cell free layer. It is observed that the resistance to the flow as well as the wall shear stress increase as the height of the stenosis increases. However, the trend is reversed as the peripheral layer thickness increases.

Modelling the spread of carrier-dependent infectious diseases with environmental effect

Many infectious diseases spread by carriers such as flies, ticks, mites, snails, etc. In this paper an SIS model for carrier-dependent infectious diseases, like cholera, diarrhea, etc. caused by direct contact of susceptibles with infectives as well as by carriers is proposed and analyzed assuming the growth of both the human and the carrier populations logistic. It is assumed further that the density of carrier population increases with the increase in the cumulative density of discharges by the human population into the environment. The mathematical model is analyzed for the following two cases: (i) the rate of cumulative environmental discharges Q is a constant, and (ii) the rate of cumulative environmental discharges Q is a function of the population density. This model is analyzed using usual theory of differential equations and computer simulation. By computer simulation it is concluded that if the growth of carrier population caused by conducive household discharges increases, the spread of the infectious disease increases.

MODELLING AND ANALYSIS OF THE SPREAD OF MALARIA: ENVIRONMENTAL AND ECOLOGICAL EFFECTS

In this paper, general SIS and SIRS models with immigration of human population for the spread of malaria are proposed and analyzed. Effects of natural as well as human population density related environmental and ecological factors, which are conductive to the survival and growth of mosquito population, are considered. It is shown in both the cases that as the parameters governing environmental and ecological factors increase, the spread of malaria increases. It is also found that due to immigration, this infectious disease becomes more endemic.

MODELING THE DRUG THERAPY FOR HIV INFECTION

A mathematical model for the effect of Reverse Transcriptase (RT) Inhibitor on the dynamics of HIV is proposed and analyzed. Further, with help of numerical simulations, the relation between efficacy of administered drug, the total number of virus particles emitted from the infected cell and the transition period is also discussed.

Modeling and Analysis of the Spread of Carrier Dependent Infectious Diseases with Environmental Effects

In this paper, SIS and SIRS models for carrier dependent infectious diseases with immigration are proposed and analyzed by considering effects of environmental and human population related factors which are conducive to the growth of carrier population. In the modeling process, the density of carrier population is governed by a general logistic model. Further, it is assumed that the growth rate per capita and the modified carrying capacity of carrier population increase as the human population density increases. In each case, it is shown that the spread of an infectious disease increases as the carrier population density increases and the disease becomes more endemic due to immigration.

Ferrofluid lubrication of cylindrical rollers with cavitation

SummaryThis paper analyses the ferrofluid lubrication of cylindrical rollers under combined rolling and normal motion. The analysis, which takes into account the rotation of magnetic particles, has been made for general cases where the magnetization vectors need not be parallel to the applied magnetic field. Cavitation boundary conditions are used and the applied magnetic field is assumed to be imposed in a direction transverse to the fluid motion. A perturbation scheme in terms of non-dimensional Brownian time relaxation parameter has been used and the effects of various parameters on bearing characteristics have been studied.