Manju Agarwal

Depletion of forestry resource biomass due to industrialization pressure: a ratio-dependent mathematical model

A model for interactions between forestry biomass, wildlife population and industrialization pressure is proposed and analysed. Here, the functional responses are assumed to be ratio-dependent type. The effect of forestry biomass depletion in a forested habitat caused by industrialization pressure on the survival of the forestry biomass dependent wildlife species is studied. The behaviours of the system near all ecological feasible equilibria are analysed.

ANALYSIS OF STABILITY AND PERSISTENCE IN A RATIO-DEPENDENT PREDATOR-PREY RESOURCE MODEL

This paper deals with a predator-prey model having ratio-dependent functional response with an additional predator resource. By means of a transformation of variables, we transform the model into a dynamical system in such a way that there is a one-to-one correspondence between the positive values of the original model and positive values of the transformed model, so that the results which are true for the transformed model are also valid for the original model. Mathematical analyses of the model equations with regard to the nature of equilibria, boundedness of solutions, and persistence are carried out. We obtain conditions which influence the boundedness and persistence of all the populations. From numerical calculations, we show that in the absence of any resource, the predator population density decreases and is less than the prey population density, but in the presence of a resource, the predator population density becomes enhanced and dominates the prey population density.

A RESOURCE-DEPENDENT COMPETITION MODEL: EFFECTS OF POPULATION PRESSURE AUGMENTED INDUSTRIALIZATION

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource. It is assumed that the growths of competing species are logistic and carrying capacities increase with increase in the density of resource biomass. Further, it is assumed that the resource biomass too is growing logistically in the environment and its carrying capacity decreases with the increase in densities of competing species and industrialization. The growth rate of population pressure is assumed to be proportional to the densities of competing species. Stabilities of all equilibria and conditions which influence the permanence of the system are carried out using theory of differential equations. Numerical simulations are performed to accomplish our analytical findings. It is shown that the equilibrium density of resource biomass decreases as (i) the growth rate coefficient of population pressure increases (ii) the growth rate coefficient of industrialization due to population pressure increases and (iii) the growth rate coefficient of industrialization due to resource biomass increases. It is found that the competitive outcome alters with increase in the growth rate coefficient of population pressure. Decrease in the equilibrium densities of competing species is also noted with increase in the growth rate coefficient of industrialization due to resource biomass.

PERSISTENCE IN A RATIO-DEPENDENT PREDATOR-PREY-RESOURCE MODEL WITH STAGE STRUCTURE FOR PREY

This paper deals with a ratio-dependent predator-prey model where the prey population is stage-structured consisting of immature and mature stages and the predator population is influenced by the resource biomass. By means of a transformation of variables, we transform the model into a dynamical system in such a way that there is one-to-one correspondence between the positive values of the original model and the positive values of the transformed model, so that the results which are true for the transformed model are also true for the original model. Dynamical behaviors such as positivity, boundedness, stability, bifurcation and persistence of the model are studied analytically using theory of differential equations. Computer simulations are carried out to substantiate the analytical findings. It is noted that the influence of the resource biomass on the predator population may lead to the extinction of prey population at a lesser value of maturity time in comparison to the absence of the resource biomass.

Harvesting and Hopf bifurcation in a prey-predator model with Holling type IV functional response

This paper aims to study the effect of Harvesting on predator species with time-delay on a Holling type-IV prey-predator model. Harvesting has a strong impact on the dynamic evolution of a population. Two delays are considered in the model of this paper to describe the time that juveniles of prey and predator take to mature. Dynamics of the system is studied in terms of local and Hopf bifurcation analysis. Finally, numerical simulation is done to support the analytical findings.

A STAGE-STRUCTURED PREDATOR–PREY MODEL WITH DENSITY-DEPENDENT MATURATION DELAY

In this paper, a stage-structured predator–prey model is proposed and analyzed with density-dependent maturation delay. We studied the dynamics of our model analytically and obtained conditions which influence the positivity and boundedness of all populations. Criteria for the existence of a non-trivial equilibrium and conditions for the uniqueness of this equilibrium are given. A linearized analysis on the equilibria, which is algebraically very complicated in the case of non-trivial equilibrium, is carried out. We proved that the system is globally asymptotically stable in the situation when non-trivial equilibrium does not exist. To accomplish our all analytical findings and to investigate the effect of density-dependent maturation delay on the system behavior, we presented a numerical simulation. It is concluded that variations in parameter, which we introduce in the system to observe the effect of density-dependent maturation delay, produces significant quantitative changes in system behavior and als...

MODELING H1N1 FLU EPIDEMIC WITH CONTACT TRACING AND QUARANTINE

A nonlinear mathematical model is proposed and analyzed to study the dynamics of 2009 H1N1 flu epidemic in a homogeneous population with constant immigration of susceptibles. The effect of contact tracing and quarantine (isolation) strategies in reducing the spread of H1N1 flu is incorporated. The model monitors the dynamics of five sub-populations (classes), namely susceptible with high infection risk, susceptible with reduction of infection risk, infective, quarantined and recovered individuals. The model analysis includes the determination of equilibrium points and carrying out their stability analysis in terms of the threshold parameter R0. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge–Kutta method along with the sensitivity analysis of the endemic equilibrium point. The analysis and numerical simulation results demonstrate that the maximum implementation of contact tracing and quarantine strategies help in reducing endemic infective class size and hence act as effective intervention strategy to control the disease. This gives a theoretical interpretation to the practical experiences that the early contact tracing and quarantine strategies are critically important to control the outbreak of epidemics.

A stage structured model of malaria transmission and efficacy of mosquito larvicides in its control

In this paper, we analyze a stage structured mathematical model for the transmission of malaria and its control by killing mosquitoes in larvae (immature) stage. Both the Mosquito and human populations are divided into susceptible and infective class. Susceptible class of mosquito population is further divided into mature and immature. The model is analyzed by using stability theory of nonlinear ordinary differential equations. Basic reproduction ratio is derived which is found to be the decreasing function of maturation delay and larvicidal activity. In addition, it is observed that biting rate of mosquito, transmission efficiency of parasitic infection from infective human to mosquito and critical value of maturation delay are the key parameters determining the stability switch in the system. Numerical simulation is also carried out to confirm the analytical results obtained in the paper.

A NUMERICAL APPROACH STUDYING THE EFFECTS OF PRECIPITATION SCAVENGING ON STEADY-STATE DISPERSION OF AIR POLLUTANTS

The present paper demonstrates the applicability of finite element method of weighted residuals to study the effects of precipitation scavenging through raindrops on the steady-state dispersion of air pollutants in the atmosphere under realistic variable wind and diffusivity profiles. Here, the washout of pollutants by rain droplets is considered and the whole analysis for the pollutant concentration is carried out in two phases viz. gaseous phase and droplet phase. The model solutions are obtained by using local basis and asymmetric quadratic weighting functions which can provide a promising alternative to the standard Galerkin formulation for problems with advective and diffusive terms. The results of the model reveal that the precipitation scavenging by rain is quite effective in cleaning the polluted atmosphere. Anticipating the need of pollutant concentration in rain drops regarding acid precipitation (or acid rain), the concentration of the absorbed pollutant in the droplet phase are also analyzed. So, the present study provides an understanding on the concentration distribution of pollutant in gaseous and droplet phases, under the effects of variable wind and diffusivity profiles.