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Shukla J.B.,Bhabha Group of Institutions | Shukla J.B.,Center for Modelling | Sundar S.,P S Institute Of Technology | Shivangi S.,Uttar Pradesh Technical University | Naresh R.,Uttar Pradesh Technical University
Natural Resource Modeling | Year: 2013

In this paper, a nonlinear mathematical model is proposed and analyzed to study the formation of acid rain in the atmosphere because of precipitation and its effect on plant species. It is considered that acid-forming gases such as SO2, NO2 emitted from various sources combine with water droplets (moisture) during precipitation and form acid rain affecting plant species. It is assumed that the biomass density of plant species follows a logistic model and its growth rate decreases with increase in the concentration of acid rain. The model is analyzed by using stability theory of differential equations and numerical simulation. The model analysis shows that as the concentration of acid rain increases because of increase in the cumulative emission rates of acid forming gases, the biomass density of plant species decreases. It is noted that if the amount of acid formed becomes very large, the plant species may become extinct. © 2012 Wiley Periodicals, Inc.


Goyal A.,University of New South Wales | Sanghi R.,Indian Institute of Technology Kanpur | Misra A.K.,Banaras Hindu University | Shukla J.B.,Bhabha Group of Institutions
Mathematical Biosciences | Year: 2013

In this paper, a non-linear mathematical model for removing an inorganic pollutant such as chromium from a water body using fungi is proposed and analyzed. It is assumed that the inorganic pollutant is discharged in a water body with a constant rate, which is depleted due to natural factors as well as by fungal absorption using dissolved oxygen in the process. The model is analyzed by using stability theory of differential equations and simulation. The analysis shows that the inorganic pollutant can be removed from the water body by fungal absorption, the rate of removal depends upon the concentration of inorganic pollutant, the density of fungal population and various interaction processes. The simulation analysis of the model confirms the analytical results. It is noted here this theoretical result is qualitatively in line with the experimental observations of one of the authors (Sanghi). © 2013 Elsevier Inc.


Shukla J.B.,Bhabha Group of Institutions | Goyal A.,University of New South Wales | Singh S.,Indian Institute of Technology Kanpur | Chandra P.,Indian Institute of Technology Kanpur
Journal of Epidemiology and Global Health | Year: 2014

In this paper, a non-linear model is proposed and analyzed to study the effects of habitat characteristics favoring logistically growing carrier population leading to increased spread of typhoid fever. It is assumed that the cumulative density of habitat characteristics and the density of carrier population are governed by logistic models; the growth rate of the former increases as the density of human population increases. The model is analyzed by stability theory of differential equations and computer simulation. The analysis shows that as the density of the infective carrier population increases due to habitat characteristics, the spread of typhoid fever increases in comparison with the case without such factors. © 2013 Ministry of Health, Saudi Arabia.


Shukla J.B.,Bhabha Group of Institutions | Sanghi R.,LNMIIT | Goyal A.,LNMIIT | Misra A.K.,Banaras Hindu University
Desalination | Year: 2011

On the planet earth, large amount of saline water (in seas and some lakes) is present and a concerted effort is needed to desalinate this water by using cheaper methods already existing in nature. Keeping this in view, a non-linear model for desalination of saline water is proposed and analyzed by using bacteria (halophiles) and marsh plants (salt grass). The system is assumed to be governed by four dependent variables namely the salt concentration, the density of halophile bacteria, the biomass density of marsh plants and the concentration of dissolved oxygen. The density of halophiles and biomass density of marsh plants are assumed to follow logistic models and their growth rates and carrying capacities increase due to interactions with salt in water. The model is analyzed by using the theory of differential equations as well as by using numerical simulation. The analysis shows that salt concentration can become very small if densities of halophiles and marsh plants are very large. The analytical result is confirmed by numerical simulation. © 2011 Elsevier B.V.


Shukla J.B.,C MEND | Shukla J.B.,Bhabha Group of Institutions | Singh V.,Banaras Hindu University | Misra A.K.,Banaras Hindu University
Nonlinear Analysis: Real World Applications | Year: 2011

An SIS model with immigration for the spread of an infectious disease with bacteria and carriers in the environment is proposed and analyzed. It is assumed that susceptibles get infected directly by infectives as well as by their contacts with bacteria discharged by infectives in the environment. The growth rate of density of bacteria is assumed to be proportional to the density of infectives and decreases naturally as well as by bacterial interactions with susceptibles and carriers. The carrier population density is considered to follow the logistic model and grows due to conducive human population density related factors. It is assumed further that the number of bacteria transported by carriers to susceptibles is proportional to densities of both bacteria and carriers. The model study shows that the spread of the infectious disease increases due to growth of bacteria and carriers in the environment and disease becomes more endemic due to immigration. © 2011 Elsevier Ltd. All rights reserved.


Misra A.K.,Banaras Hindu University | Sharma A.,Banaras Hindu University | Shukla J.B.,Bhabha Group of Institutions
BioSystems | Year: 2015

The impact of awareness campaigns and behavioral responses on epidemic outbreaks has been reported at times. However, to what extent does the provision of awareness and behavioral changes affect the epidemic trajectory is unknown, but important from the public health standpoint. To address this question, we formulate a mathematical model to study the effect of awareness campaigns by media on the outbreak of an epidemic. The awareness campaigns are treated as an intervention for the emergent disease. These awareness campaigns divide the whole populations into two subpopulation; aware and unaware, by inducing behavioral changes amongst them. The awareness campaigns are included explicitly as a separate dynamic variable in the modeling process. The model is analyzed qualitatively using stability theory of differential equations. We have also identified an optimal implementation rate of awareness campaigns so that disease can be controlled with minimal possible expenditure on awareness campaigns, using optimal control theory. The control setting is investigated analytically using optimal control theory, and the numerical solutions illustrating the optimal regimens under various assumptions are also shown. © 2015 Elsevier Ireland Ltd.


Misra A.K.,Banaras Hindu University | Lata K.,Banaras Hindu University | Shukla J.B.,Bhabha Group of Institutions
International Journal of Modeling, Simulation, and Scientific Computing | Year: 2014

In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of forestry resources caused simultaneously by population and population pressure augmented industrialization. The control of population pressure, using economic efforts is also considered in the modeling process. It is assumed that cumulative biomass density of forestry resources and the density of population follow logistic models. It is further assumed that the density of population and the level of industrialization increase as the cumulative biomass density of forestry resources increases. The cumulative density of economic efforts, which are applied to control the population pressure, is considered to be proportional to the population pressure. The model analysis shows that as the population pressure increases, the level of industrialization increases leading to decrease in the cumulative biomass density of forestry resources. It is found that if population pressure is controlled by using some economic efforts, the decrease in cumulative biomass density of forestry resources can be made much less than the case when no control is applied. It is also noted that if the population pressure augmented industrialization increases without control, the forestry resources may become extinct. © 2014 World Scientific Publishing Company.


Misra A.K.,Banaras Hindu University | Sharma A.,Banaras Hindu University | Shukla J.B.,Bhabha Group of Institutions
Mathematical and Computer Modelling | Year: 2011

In this paper, a non-linear mathematical model for the effects of awareness programs on the spread of infectious diseases such as flu has been proposed and analyzed. In the modeling process it is assumed that disease spreads due to the contact between susceptibles and infectives only. The growth rate of awareness programs impacting the population is assumed to be proportional to the number of infective individuals. It is further assumed that due to the effect of media, susceptible individuals form a separate class and avoid contact with the infectives. The model is analyzed by using stability theory of differential equations. The model analysis shows that the spread of an infectious disease can be controlled by using awareness programs but the disease remains endemic due to immigration. The simulation analysis of the model confirms the analytical results. © 2010 Elsevier Ltd.


Misra A.K.,Banaras Hindu University | Lata K.,Banaras Hindu University | Shukla J.B.,Bhabha Group of Institutions
Environment, Development and Sustainability | Year: 2014

In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of forest resources caused by population and the corresponding population pressure. It is assumed that the cumulative density of forest resources and the density of populations follow logistic models with prey-predator type nonlinear interaction terms. It is considered that the carrying capacity of forest resources decreases by population pressure, the main focus of this paper. A conservation model is also proposed to control the population pressure by providing some economic incentives to people, the amount of which is assumed to be proportional to the population pressure. The model is analyzed by using stability theory of differential equations and numerical simulation. The model analysis shows that as the density of population or population pressure increases, the cumulative density of forest resources decreases, and the resources may become extinct if the population pressure becomes too large. It is also noted that by controlling the population pressure, using some economic incentives, the density of forest resources can be maintained at an equilibrium level, which is population density dependent. The simulation analysis of the model confirms analytical results. © 2013 Springer Science+Business Media Dordrecht.


PubMed | Banaras Hindu University and Bhabha Group of Institutions
Type: | Journal: Bio Systems | Year: 2015

The impact of awareness campaigns and behavioral responses on epidemic outbreaks has been reported at times. However, to what extent does the provision of awareness and behavioral changes affect the epidemic trajectory is unknown, but important from the public health standpoint. To address this question, we formulate a mathematical model to study the effect of awareness campaigns by media on the outbreak of an epidemic. The awareness campaigns are treated as an intervention for the emergent disease. These awareness campaigns divide the whole populations into two subpopulation; aware and unaware, by inducing behavioral changes amongst them. The awareness campaigns are included explicitly as a separate dynamic variable in the modeling process. The model is analyzed qualitatively using stability theory of differential equations. We have also identified an optimal implementation rate of awareness campaigns so that disease can be controlled with minimal possible expenditure on awareness campaigns, using optimal control theory. The control setting is investigated analytically using optimal control theory, and the numerical solutions illustrating the optimal regimens under various assumptions are also shown.

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