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

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International Journal of Modeling, Simulation, and Scientific Computing 2012年第1期3卷 51-67页

作者： manju agarwal ABHINAV TANDON Department of Mathematics and Astronomy University of Lucknow LucknowUttar PradeshIndia Department of Mathematics Shri Ramswaroop Memorial Group of Professional Colleges Tiwariganj Faizabad RoadLucknowUttar PradeshIndia

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 ***,the washout of pollutants by rain droplets is considered and the whole analysis for the pollutant concentration is carried out in two phases *** phase and droplet *** 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 *** results of the model reveal that the precipitation scavenging by rain is quite effective in cleaning the polluted *** 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 ***,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.

关键词： Precipitation scavenging pollutant gaseous phase droplet phase finite element asymmetric weighting functions

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

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International Journal of Modeling, Simulation, and Scientific Computing 2014年第4期5卷 201-226页

作者： manju agarwal Archana S.Bhadauria Department of Mathematics&Astronomy Lucknow University Lucknow 226007 Uttar PradeshIndia

In this paper,we analyze a stage structured mathematical model for the transmission of malaria and its control by killing mosquitoes in larvae(immature)*** the Mosquito and human populations are divided into susceptible and infective ***-ceptible class of mosquito population is further divided into mature and *** model is analyzed by using stability theory of nonlinear ordinary differential *** reproduction ratio is derived which is found to be the decreasing function of maturation delay and larvicidal *** 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 *** simulation is also carried out to confirm the analytical results obtained in the paper.

关键词： Mosquitoes adults immature mature bifurcation larvicides

Conservation of Forestry Biomass with the Use of Alternative Resource

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Open Journal of Ecology 2015年第4期5卷 87-109页

作者： manju agarwal Rachana Pathak Department of Mathematics & Astronomy Lucknow University Lucknow India

The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrialization pressure, toxicant pressure and technological effort is proposed and analysed. We find out the critical value of delay and observe that there is Hopf bifurcation. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations are given to illustrate the analytical results.

关键词： Forestry Biomass Industrialization Alternative Resource Toxicant Technological Effort Local Stability Hopf Bifurcation

MODELING H1N1 FLU EPIDEMIC WITH CONTACT TRACING AND QUARANTINE

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International Journal of Biomathematics 2012年第5期5卷 83-101页

作者： manju agarwal ARCHANAS. BHADAURIA Department of Mathematics ~ Astronomy Lucknow University Lucknow-226007 Uttar Pradesh India

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 reduc ing 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 numeri cal 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 interpreta tion to the practical experiences that the early contact tracing and quarantine strategies are critically important to control the outbreak of epidemics.

关键词： Runge-Kutta方法追踪流感检疫疫情非线性数学模型地方病平衡点建模

Mathematical Modeling and Analysis of Tumor Therapy with Oncolytic Virus

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Applied Mathematics 2011年第1期2卷 131-140页

作者： manju agarwal Archana S. Bhadauria 不详

In this paper, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equa- tions. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge- Kutta method which supports the theoretical findings. It is found that both infected and uninfected tumor cells and hence tumor load can be eliminated with time, and complete recovery is possible because of virus therapy, if certain conditions are satisfied. It is further found that the system appears to exhibit periodic limit cycles and chaotic attractors for some ranges of the system parameters.

关键词： Tumor Oncolytic Virus Limit Cycles Chaotic Behavior Attractors Asymptotic Stability

EFFECTS OF POPULATION AND INDUSTRIALIZATION ON THE DEGRADATION OF BIOMASS AND ITS REGENERATION BY AFFORESTATION: A MATHEMATICAL MODEL

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生物数学学报 1988年第1期 1-9页

作者： J.B.Shukla V.N.Pal O.P.Misra manju agarwal Ajai Shukla Departmant of Mathematics I.I.T Kanpur India Departmant of Applied Science Institute of Eng.and Techn Lucknow Nodal Centre for National Technical Manpower Information System I. I. T. Kanpur India

The bio-mass(Food, Fodder and Forestry, etc. ) in a habitat has beencontinuously depleting due to rapid industrialization and over-population leadingto various kinds of undesirable effects on our environment and on land masscausing deep concern to planners and management experts. In this paper, therefore, a mathematical model for degradation of bio-massis presented to study the effects of industrialization and associated growth ofpopulation, It is shown that with the increase in the levels of these factors,the bio-mass resource may not last long. It has also been pointed out mathematicallythat the level of the biomass can be maintained at desired equilibrium level bya suitable afforestation programme.

关键词： A MATHEMATICAL MODEL EFFECTS OF POPULATION AND INDUSTRIALIZATION ON THE DEGRADATION OF BIOMASS AND ITS REGENERATION BY AFFORESTATION