Browsing by Author "A.K. Misra"

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A Delay Mathematical Model for the Control of Unemployment
(2013) A.K. Misra; Arvind K. Singh
In this paper, we have proposed and analyzed a nonlinear mathematical model for control of unemployment in the developing countries by incorporating time delay in creating new vacancies. In the modeling process, three dynamic variables have been considered, namely, (i) number of unemployed persons, (ii) number of employed persons, and (iii) number of newly created vacancies. The model is studied using stability theory of differential equations. It is found that the model has only one equilibrium, which is stable in absence of delay. It is further shown that this stable equilibrium becomes unstable as delay crosses some critical value. This critical value of delay has been obtained analytically. Further, direction of Hopf bifurcation and stability of the bifurcating periodic solutions are studied by applying the normal form theory and the center manifold theorem. Numerical simulation of the model has been carried out to illustrate the analytical results. © 2013 Foundation for Scientific Research and Technological Innovation.
A delay mathematical model for the spread and control of water borne diseases
(2012) A.K. Misra; Vishal Singh
A non-linear SIRS mathematical model to explore the dynamics of water borne diseases like cholera is proposed and analyzed by incorporating delay in using disinfectants to control the disease. It is assumed that the only way for the spread of infection is ingestion of contaminated water by susceptibles. As the pathogens discharged by infectives reach to the aquatic environment, it is assumed that the growth rate of pathogens is proportional to the number of infectives. Further, it is assumed that disinfectants are introduced to kill pathogens with a rate proportional to the density of pathogens in the aquatic environment. The model is analyzed by using stability theory of delay differential equations. It is found that the model exhibits two equilibria, the disease free equilibrium and the endemic equilibrium. The analysis shows that under certain conditions, the cholera disease may be controlled by using disinfectants but a longer delay in their use may destabilize the system. Numerical simulation is also carried out to confirm the analytical results. © 2012 Elsevier Ltd.
A mathematical model for control of vector borne diseases through media campaigns
(2013) A.K. Misra; Anupama Sharma; Jia Li
Vector borne diseases spread rapidly in the population. Hence their control intervention must work quickly and target large area as well. A rational approach to combat these diseases is mobilizing people and making them aware through media campaigns. In the present paper, a non-linear mathematical model is proposed to assess the impact of creating awareness by the media on the spread of vector borne diseases. It is assumed that as a response to awareness, people will not only try to protect themselves but also take some potential steps to inhibit growth of vectors in the environment. The model is analyzed using stability theory of differential equations and numerical simulation. The equilibria and invasion threshold for infection i.e., basic reproduction number, has been obtained. It is found that the presence of awareness in the population makes the disease invasion dificult. Also, continuous efforts by the media along with the swift dissemination of awareness can completely eradicate the disease from the system.
A mathematical model for the conservation of forestry resources with two discrete time delays
(Springer Science and Business Media Deutschland GmbH, 2017) Kusum Lata; A.K. Misra; R.K. Upadhyay
Forests are very important for the life on the planet earth. Now-a-days, depletion of forestry resources is a serious problem across the world and there is a need to make some efforts to conserve them. For this, in the present study, we have formulated a nonlinear mathematical model to assess the effect of applied technological efforts on the conservation of forestry resources with two discrete time delays. The first time delay is involved in applying technological efforts whereas the second one is responsible for the visibility of applied technological efforts on the growth of forestry resources. The conditions for local stability are obtained and it is shown that periodic solutions arise through Hopf-bifurcation as the time delay crosses some threshold value. Further, it is noted that the stable equilibrium may become unstable due to the increase in the value of second delay parameter. Numerical simulation is also performed to support the analytically obtained results. © 2017, Springer International Publishing AG.
A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay
(Elsevier Ltd, 2013) A.K. Misra; S.N. Mishra; A.L. Pathak; P.K. Srivastava; Peeyush Chandra
In this paper, a non-linear delay mathematical model for the control of carrier-dependent infectious diseases through insecticides is proposed and analyzed. In the modeling process, it is assumed that disease spreads due to direct contact between susceptibles and infectives as well as through carriers (indirect contact). Further, it is assumed that insecticides are used to kill carriers and the rate of introduction of insecticides is proportional to the density of carriers with some time lag. The model analysis suggests that as delay in using insecticides exceeds some critical value, the system loses its stability and Hopf-bifurcation occurs. The direction, stability and period of the bifurcating periodic solutions arising through Hopf-bifurcation are also analyzed using normal form concept and center manifold theory. Numerical simulation is carried out to confirm the obtained analytical results. © 2013 Elsevier Ltd. All rights reserved.
A Mathematical Model for the Control of Infectious Diseases: Effects of TV and Radio Advertisements
(World Scientific Publishing Co. Pte Ltd, 2018) A.K. Misra; Rajanish Kumar Rai
The broadcast of awareness programs through TV and radio advertisements (ads) makes people aware and brings behavioral changes among the individuals regarding the risk of infection and its control mechanisms. In this paper, we propose and analyze a nonlinear mathematical model for the control of infectious diseases due to impact of TV and radio advertisements. It is assumed that susceptible individuals are vulnerable to infection as well as information through TV and radio ads and they contract infection via direct contact with infected individuals. In the model formulation, it is also assumed that the growth rates in cumulative number of TV and radio ads are proportional to the number of infected individuals with decreasing function of aware individuals. Further, it is assumed that awareness among susceptible individuals induces behavioral changes and they form separate aware classes, which are fully protected from infection as they use precautionary measures for their protection during the infection period. The feasibility of equilibria and their stability properties are discussed. It is shown that the augmentation in dissemination rate of awareness among susceptible individuals due to TV and radio ads may cause stability switches through Hopf-bifurcation. The analytical findings are supported through numerical simulations. © 2018 World Scientific Publishing Company.
A mathematical model for the depletion of forestry resources due to population and population pressure augmented industrialization
(World Scientific Publishing Co. Pte Ltd, 2014) A.K. Misra; Kusum Lata; J.B. Shukla
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.
A mathematical model for the removal of pollutants from the atmosphere through artificial rain
(Taylor and Francis Ltd., 2022) Amita Tripathi; A.K. Misra; J.B. Shukla
To reduce the pollution from the atmosphere or polluted cities like the capital city Delhi of India, use of artificial rain is a solution. In this paper, we have proposed and analyzed a nonlinear mathematical model to reduce the pollution level by rain making. In the proposed model five variables are considered, namely; (i) number density of water vapor, (ii) number density of cloud drops, (iii) number density of raindrops, (iv) cumulative concentration of aerosols, and (v) concentration of pollutant particles suspended in the region of consideration. The effect of environmental fluctuations has been studied with the help of Lyapunov functionals. The model is analyzed in the presence of white noise and proved that if rain persists, the pollutants can be totally washed out. It has been observed that the environmental disturbances are not much favorable in such experiments as the presence of environmental disturbance may destabilize the system. It is found that to remove pollutants completely, it is necessary to prevent the formation of pollutants. The simulation is performed to support the analytical findings. © 2021 Taylor & Francis Group, LLC.
A mathematical model for unemployment
(2011) A.K. Misra; Arvind K. Singh
In this paper we have proposed and analyzed a non-linear mathematical model for unemployment by considering three variables, namely the numbers of unemployed, temporarily employed and regularly employed persons. The model is studied using the stability theory of differential equations. It is found that the model has only one equilibrium, which is non-linearly stable under certain conditions. Numerical simulation of the model has been carried out to confirm the analytical results. © 2010 Published by Elsevier Ltd. All rights reserved.
A mathematical model to achieve sustainable forest management
(World Scientific Publishing Co. Pte Ltd, 2015) A.K. Misra; Kusum Lata
Forest resources are important natural resources for all living beings but they are continuously depleting due to overgrowth of human population and their development activities. Therefore, conservation of forest resources is an important problem for sustainable development. In view of this, in this paper, we have proposed and analyzed a nonlinear mathematical model to study the effects of economic and technological efforts on the conservation of forest resources. In the modeling process, it is assumed that due to increase in population size, the demand of population (population pressure) for forest products, lands, etc., increases and to reduce this population pressure, economic efforts are employed proportional to the population pressure. Further, it is assumed that technological efforts in the form of genetically engineered plants are applied proportional to the depleted level of forest resources to conserve them. Model analysis reveals that increase in economic and technological efforts increases the density of forest resources but further increase in these efforts destabilizes the system. Numerical simulation is carried out to verify analytical findings and explore the effect of different parameters on the dynamics of model system. © 2015 World Scientific Publishing Company.
A mathematical model to study the dynamics of carbon dioxide gas in the atmosphere
(2013) A.K. Misra; Maitri Verma
A nonlinear mathematical model to explore the effects of human population and forest biomass on the dynamics of atmospheric carbon dioxide (CO 2) gas has been proposed and analyzed. In the modeling process, it is assumed that the concentration of CO2 in the atmosphere increases due to natural as well as anthropogenic factors. Further, it is assumed that the atmospheric CO2 is absorbed by forest biomass and other natural sinks. Equilibria of the model have been obtained and their stability discussed. The model analysis reveals that human population declines with an increase in anthropogenic CO2 emissions into the atmosphere. Further, it is found that the depletion of forest biomass due to human population (deforestation) leads to increase in the atmospheric concentration of CO2. It is also found that deforestation rate coefficient has destabilizing effect on the dynamics of the system and if it exceeds a threshold value, the system loses its stability and periodic solutions may arise through Hopf-bifurcation. The stability and direction of these bifurcating periodic solutions are analyzed by using center manifold theory. Numerical simulation is performed to support theoretical results. © 2013 Elsevier Inc.
A model for the effect of density of human population on the depletion of dissolved oxygen in a water body
(Kluwer Academic Publishers, 2015) A.K. Misra; P.K. Tiwari
A nonlinear mathematical model to study the effect of density of human population on the depletion of dissolved oxygen in a water body is proposed and analyzed. The proposed model is governed by interactions among five dependent variables, namely density of resource biomass, density of human population, concentration of organic pollutants, density of bacteria and concentration of dissolved oxygen. In the model formulation, it is assumed that density of resource biomass and density of human population follow logistic models with prey--predator type interaction. The model is analyzed using stability theory of differential equations. The analysis of model shows that increase in human population intensify the depletion in concentration of dissolved oxygen in a water body. Numerical simulations are carried out to illustrate analytical findings. © 2014, Springer Science+Business Media Dordrecht.
A modeling study on the role of fungi in removing inorganic pollutants
(2013) Ashish Goyal; Rashmi Sanghi; A.K. Misra; J.B. Shukla
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.
A nonlinear mathematical model to study the interactions of hot gases with cloud droplets and raindrops
(2009) Shyam Sundar; Ram Naresh; A.K. Misra; J.B. Shukla
In this paper, a nonlinear mathematical model is proposed and analyzed to study the interactions of hot gases with cloud droplets as well as with raindrops and their removal by rain from the stable atmosphere. The atmosphere, during rain, is assumed to consist of five nonlinearly interacting phases i.e. the vapour phase, the phase of cloud droplets, the phase of raindrops, the phase of hot gaseous pollutants and the absorbed phase of hot gases in the raindrops (if it exists). It is further assumed that these phases undergo ecological type growth and nonlinear interactions. The proposed model is analyzed using stability theory of differential equations and by numerical simulation. It is shown that the cumulative concentration of gaseous pollutants decreases due to rain and its equilibrium level depends upon the density of cloud droplets, the rate of formation of raindrops, emission rate of pollutants, the rate of falling absorbed phase on the ground, etc. It is noted here that if gases are very hot, cloud droplets are not formed and rain may not take place. In such a case gaseous pollutants may not be removed from the atmosphere due to non-occurrence of rain. © 2008 Elsevier Inc. All rights reserved.
A ratio-dependent predator-prey model with delay and harvesting
(2010) A.K. Misra; B. Dubey
In this paper a predator-prey model with discrete delay and harvesting of predator is proposed and analyzed by considering ratio-dependent functional response. Conditions of existence of various equilibria and their stability have been discussed. By taking delay as a bifurcation parameter, the system is found to undergo a Hopf bifurcation. Numerical simulations are also performed to illustrate the results. © 2010 World Scientific Publishing Company.
A reaction-diffusion model for the control of cholera epidemic
(World Scientific Publishing Co. Pte Ltd, 2016) A.K. Misra; Alok Gupta
Understanding the spatio-temporal dynamics of cholera outbreaks may help in devising more effective control procedures. In this paper, we have considered a reaction-diffusion system for biological control of cholera epidemic. Firstly, we have focused on temporal evolution of cholera in a region and its control using lytic bacteriophage in the aquatic reservoirs. Then, we have explored the effect of spatial dispersion of populations on the disease dynamics. We have observed the onset of sustained oscillations via Hopf-bifurcation for the endemic state of temporal system. This onset of fluctuations in populations depends upon the phage adsorption rate. But in the spatially extended setting, all the populations stabilize i.e., the spatio-temporal distribution of all the populations becomes uniform. Some numerical computations have been done to verify analytical results. © 2016 World Scientific Publishing Company.
A robust role of carbon taxes towards alleviating carbon dioxide: a modeling study
(Springer Science and Business Media B.V., 2024) Anjali Jha; A.K. Misra
Carbon tax serves as a tool to discourage carbon dioxide (CO2) emissions, which are a root cause of climate change. A well-designed tax policy could reduce the risk of climate change, promote innovation in carbon-reducing technologies, and increase public revenue. In this research work, the model formulation is based on dynamic interactions among variables, namely the atmospheric concentration of CO2, human population, forestry biomass, and the levied carbon tax. We assume that the collected revenue is used to control anthropogenic emissions of CO2 and fund reforestation/afforestation programs. We have derived sufficient conditions under which the considered dynamical variables settle to their equilibrium levels. The model analysis reveals that the atmospheric level of CO2 decreases as the levied tax rate increases, indicating that the atmospheric CO2 level can be reversed from its present state through the imposition of a carbon tax. Additionally, the formulated system undergoes Hopf-bifurcation concerning the growth of the levied tax and deforestation rate. Furthermore, through simulations, we have demonstrated that utilizing tax revenues for technologies that limit human-induced CO2 emissions and reforestation/afforestation programs is a promising strategy for mitigating the increased levels of CO2. © The Author(s), under exclusive licence to Springer Nature B.V. 2024.
A stochastic model for making artificial rain using aerosols
(Elsevier B.V., 2018) A.K. Misra; Amita Tripathi
In this paper, a nonlinear deterministic mathematical model along with its stochastic version for artificial rain is proposed and analyzed. We have considered three dynamical variables in the modeling process; namely (i) density of cloud droplets, (ii) density of raindrops, and (iii) concentration of mixture of conducive aerosols. It is assumed that the cloud droplets are continuously formed in the atmosphere at a constant rate but its conversion into raindrops does not take place in the same proportion. The artificially introduced aerosols increase the rate of formation of raindrops from cloud droplets. These aerosols are introduced in the regional atmosphere at a rate proportional to the density of cloud droplets. The proposed model is analyzed using stability theory of differential equations in deterministic as well as stochastic environment. Numerical simulation is performed to see the effect of important parameters on the process leading to rainfall. © 2018 Elsevier B.V.
Allocation of hospital beds on the emergence of new infectious disease: A mathematical model
(American Institute of Physics Inc., 2023) A.K. Misra; Jyoti Maurya
This paper is concerned to a mathematical model for the management of hospital beds when a new infection emerges in the population with the existing infections. The study of this joint dynamics presents formidable mathematical challenges due to a limited number of hospital beds. We have derived the invasion reproduction number, which investigates the potential of a newly emerged infectious disease to persist when some infectious diseases are already invaded the host population. We have shown that the proposed system exhibits transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations under certain conditions. We have also shown that the total number of infected individuals may increase if the fraction of the total number of hospital beds is not properly allotted to the existing and a newly emerged infectious disease. The analytically obtained results are verified with the help of numerical simulations. © 2023 Author(s).
An optimal control problem for carrier dependent diseases
(Elsevier Ireland Ltd, 2020) Kusum Lata; S.N. Mishra; A.K. Misra
In developing countries, several diseases spread in human population due to the abundance of houseflies (a kind of carrier). The main reason behind the spread of these diseases is the lack of awareness among peoples regarding the sanitation practices and economic constraints. To understand the dynamics of the spread and control of these diseases, in this paper, we propose a mathematical model by considering logistic growth of houseflies. In the model formulation, it is assumed that houseflies transport the bacteria responsible for the disease transmission from the environment to the edibles of human population. To reduce the density of houseflies and number of infected individuals, an optimization problem is also formulated and analyzed. Numerical simulations are performed to support analytically obtained results. © 2019 Elsevier B.V.