Browsing by Author "Maitri Verma"

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A DELAY NONAUTONOMOUS PREDATOR-PREY MODEL for the EFFECTS of FEAR, REFUGE and HUNTING COOPERATION
(World Scientific, 2021) Pankaj Kumar Tiwari; Maitri Verma; Soumitra Pal; Yun Kang; Arvind Kumar Misra
Fear of predation may assert privilege to prey species by restricting their exposure to potential predators, meanwhile it can also impose costs by constraining the exploration of optimal resources. A predator-prey model with the effect of fear, refuge, and hunting cooperation has been investigated in this paper. The system's equilibria are obtained and their local stability behavior is discussed. The existence of Hopf-bifurcation is analytically shown by taking refuge as a bifurcation parameter. There are many ecological factors which are not instantaneous processes, and so, to make the system more realistic, we incorporate three discrete time delays: in the effect of fear, refuge and hunting cooperation, and analyze the delayed system for stability and bifurcation. Moreover, for environmental fluctuations, we further modify the delayed system by incorporating seasonality in the fear, refuge and cooperation. We have analyzed the seasonally forced delayed system for the existence of a positive periodic solution. In the support of analytical results, some numerical simulations are carried out. Sensitivity analysis is used to identify parameters having crucial impacts on the ecological balance of predator-prey interactions. We find that the rate of predation, fear, and hunting cooperation destabilizes the system, whereas prey refuge stabilizes the system. Time delay in the cooperation behavior generates irregular oscillations whereas delay in refuge stabilizes an otherwise unstable system. Seasonal variations in the level of fear and refuge generate higher periodic solutions and bursting patterns, respectively, which can be replaced by simple 1-periodic solution if the cooperation and fear are also allowed to vary with time in the former and latter situations. Higher periodicity and bursting patterns are also observed due to synergistic effects of delay and seasonality. Our results indicate that the combined effects of fear, refuge and hunting cooperation play a major role in maintaining a healthy ecological environment. © 2021 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.
Capturing the interplay between malware and anti-malware in a computer network
(2014) A.K. Misra; Maitri Verma; Anupama Sharma
In an era with affluence of local area networks, the recurrent attacks of viruses and other malicious objects are undoubtedly an intruding threat. These malicious objects spread quickly through an unprotected network, corrupt the data and harm the nodes. To comprehend this problem and its plausible solutions more thoroughly, we have proposed and analyzed a mathematical model by considering a network in which nodes are either infected or prone to it. It is considered that nodes vulnerable to infection become infected, when attacked by malicious objects present in the network. To minimize the abundance of malicious objects and infected nodes, some anti-malware softwares are installed in the network, which are continuously being updated. On analyzing the proposed model, we obtained two equilibria and a threshold governing the dynamics of malicious objects in a computer network. The characterization of stability behavior of obtained equilibria is also discussed in detail. The numerical simulation illustrates the validity of analytically obtained results. © 2013 Elsevier Inc. All rights reserved.
Effect of global warming on sea level rise: A modeling study
(Elsevier B.V., 2017) J.B. Shukla; Maitri Verma; A.K. Misra
Global mean sea level has been rising in response to global warming since the past few decades and is anticipated to potentially affect the coastal population. The main driver of global warming is the enhanced concentration of the heat-trapping gas carbon dioxide in the atmosphere. In this paper, we propose a nonlinear mathematical model to study the effect of an increase in the anthropogenic carbon dioxide emissions on sea level rise and its effect on the human population. The long-term behavior of the proposed system is analyzed using stability theory of differential equations. The model analysis shows that an increase in the anthropogenic emission rate of carbon dioxide leads to increase in the equilibrium levels of surface temperature and sea water level. Further, it is found that the increase in anthropogenic emission rate of carbon dioxide and melting rate of ice sheets lead to decrease in the equilibrium level of human population as a result of crowding caused by the decrease in the total inhabitable land area due to sea level rise. Numerical simulations are carried out to illustrate the effect of key parameters on the dynamics of the system. © 2017 Elsevier B.V.
Effects of elevated carbon dioxide and temperature on crop yield: a modeling study
(Springer Verlag, 2018) Maitri Verma; A.K. Misra
Food security is one of the burning issues at present. The elevated levels of atmospheric carbon dioxide (CO 2) and temperature are anticipated to affect the yield of staple food crops. In this paper, we have formulated a nonlinear mathematical model to study the crop response to the elevated levels of CO 2 and temperature. Qualitative analysis of the model is performed to assess the long-term behavior of the system. The model analysis provides a condition under which the increase in anthropogenic CO 2 emission leads to decrease in the equilibrium level of crop yield. The analytical results are validated through numerical simulation for the case of wheat yield in India. The future projections of wheat yield in India are depicted in various scenarios. Sensitivity analysis is performed to explore the effect of changes in the key parameters on the wheat yield. © 2017, Korean Society for Computational and Applied Mathematics.
Impact of environmental education on mitigation of carbon dioxide emissions: A modelling study
(Inderscience Enterprises Ltd., 2015) A.K. Misra; Maitri Verma
Human activities have contributed significantly to the menace of global warming by enhancing the atmospheric level of carbon dioxide (CO2). Environmental education is an avenue to persuade people to reduce their CO2 emissions. Comprehension of the impact of environmental education on the reduction of CO2 emissions aids in devising effectual environmental education policies. In this view, we have formulated a non-linear mathematical model to study the impact of educational programmes on the abatement of CO2 emissions. It is considered that the educational programmes are implemented at a rate proportional to the increase in atmospheric concentration of CO2 due to human activities. Model is analysed by using stability theory of differential equations. Model analysis reveals that the educational programmes are helpful in reduction of anthropogenic CO2 emissions. But if reduction rate of carbon footprint by educated people is small, increase in execution rate of educational programmes and/or dissemination rate of education among people cannot effectively curtail CO2 emissions. Moreover, for high values of reduction rate coefficient of carbon footprint, atmospheric concentration of CO2 may not get stabilised. Numerical simulation is carried out to illustrate the theoretical findings. Copyright © 2015 Inderscience Enterprises Ltd.
Mathematical modeling and optimal control of carbon dioxide emissions from energy sector
(Springer Science and Business Media B.V., 2021) Maitri Verma; Alok Kumar Verma; A.K. Misra
Energy demand is rising day by day and will continue to increase to meet the demand of the growing population. A major portion of global energy production comes from fossil fuel burning, resulting in the increase in the atmospheric burden of global warming gas carbon dioxide (CO2). Cutting down CO2 emission from the energy sector is crucial to meet the climate change mitigation target. This paper is focused on fulfilling two objectives: The first objective is to present a mathematical model that captures the dynamical relationship between the human population, energy use, and atmospheric carbon dioxide, and the second aim is to derive a mathematical framework to effectively utilize the available mitigation options to curtail CO2 emission from energy use by proposing an optimal control problem. The mitigation options that reduce the CO2 emission rate from energy production, as well as the options that reduce the energy consumption rate, are considered in the modeling process. The proposed mathematical model is analyzed qualitatively to comprehend the system’s long-term behavior. The model parameters are fitted to real data of global energy use, population, and CO2 concentration. It is shown that the equilibrium level of CO2 reduces with the increase in the efficiencies of mitigation options to reduce the CO2 emission rate per unit energy use and energy consumption rate. The optimality system is derived analytically by taking the efficiencies of the mitigation options to reduce the CO2 emission rate and energy consumption rate as control variables. Numerical simulations are conducted to validate the theoretical findings and identify the optimal profiles of control variables under different settings of CO2 emission rate, energy consumption rate, and maximum efficiencies of available mitigation options to cut down CO2 emission rate and energy consumption rate. It is found that the development and implementation of more efficient mitigation options and switching to low carbon energy sources bring reduction in the mitigation cost. © 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature.
Modeling the control of atmospheric carbon dioxide through reforestation: effect of time delay
(Springer Science and Business Media Deutschland GmbH, 2015) A.K. Misra; Maitri Verma; Ezio Venturino
Carbon dioxide (CO 2) is the prime greenhouse gas responsible for the threat of global warming. Forest biomass plays an important role in sequestration of carbon dioxide from the atmosphere but the global forest biomass is declining with an alarming rate due to human activities. In this scenario, reforestation is crucial to reduce the atmospheric burden of CO 2. In this paper, we propose a nonlinear mathematical model to study the effect of reforestation as well as the delay involved in between the measurement of forest data and implementation of reforestation efforts on the control of atmospheric concentration of CO 2. Model analysis shows that the atmospheric concentration of CO 2 decreases due to reforestation but a longer delay in between measurement of forest biomass and implementation of reforestation efforts has destabilizing effect on the dynamics of the system. The critical value of this time delay is found analytically. The Hopf-bifurcation analysis is performed by taking time delay as bifurcation parameter. The stability and direction of bifurcating periodic solutions arising through Hopf-bifurcations are also discussed. © 2015, Springer International Publishing Switzerland.
Modeling the Effect of Prey Refuge on a Ratio-Dependent Predator–Prey System with the Allee Effect
(Springer New York LLC, 2018) Maitri Verma; A.K. Misra
The extinction of species is a major threat to the biodiversity. The species exhibiting a strong Allee effect are vulnerable to extinction due to predation. The refuge used by species having a strong Allee effect may affect their predation and hence extinction risk. A mathematical study of such behavioral phenomenon may aid in management of many endangered species. However, a little attention has been paid in this direction. In this paper, we have studied the impact of a constant prey refuge on the dynamics of a ratio-dependent predator–prey system with strong Allee effect in prey growth. The stability analysis of the model has been carried out, and a comprehensive bifurcation analysis is presented. It is found that if prey refuge is less than the Allee threshold, the incorporation of prey refuge increases the threshold values of the predation rate and conversion efficiency at which unconditional extinction occurs. Moreover, if the prey refuge is greater than the Allee threshold, situation of unconditional extinction may not occur. It is found that at a critical value of prey refuge, which is greater than the Allee threshold but less than the carrying capacity of prey population, system undergoes cusp bifurcation and the rich spectrum of dynamics exhibited by the system disappears if the prey refuge is increased further. © 2018, Society for Mathematical Biology.
Modeling the effects of psychological fear and media-induced awareness on the dynamics of infectious diseases
(American Institute of Mathematical Sciences, 2024) A.K. Misra; Kuldeep Kumar Tripathi; Maitri Verma
The outbreak of an infectious disease in a community creates psychological fear in the population that stimulates the individuals to adopt appropriate behavioral changes to reduce the risk of contracting the infection. The awareness created by mass media is another important factor that motivates people to comply with the precautionary measures required to inhibit the transmission of disease. A study of the combined effects of psychological fear and media-induced awareness on the transmission dynamics of an infectious disease is crucial for designing strategies to control the spread of the infectious disease in a community. This work presents a mathematical model to assess the combined effects of fear and media advertisements on the dynamics of infectious diseases. The stability properties of the solutions of the proposed system are investigated. It is found that if the growth rate of media advertisements exceeds a threshold value, the system enters into limit cycle oscillations from stable equilibrium via Hopf-bifurcation. The amplitude of these periodic oscillations increases with the increase in the growth rate of media advertisements. An increase in the degree of fear in the community may dampen the amplitude of periodic oscillations and above a threshold value of the fear factor, the periodic oscillations die out and endemic equilibrium gets stabilized. It is also found that the high level of fear reduces the effect of the increase in the growth rate of media advertisements and the dissemination rate of awareness among susceptible individuals on the control of infection in the population. © 2024 American Institute of Mathematical Sciences. All rights reserved.
Modeling the effects of psychological fear, media-induced awareness, and sanitation efforts on the dynamics of bacterial diseases
(Springer Science and Business Media Deutschland GmbH, 2025) Kuldeep Kumar Tripathi; Maitri Verma; Arvind Kumar Misra
Bacterial diseases significantly impact human health and the economy, posing serious challenges to societal well-being. Psychological fear of infection motivates behavioral changes to reduce contacts with infected individuals. Awareness campaigns play a crucial role in educating the public about precautionary measures, thereby reducing the likelihood of bacteria ingestion from contaminated sources. Furthermore, individuals who are informed through such campaigns often implement sanitation practices that help to reduce bacterial density in the environment. This study develops a nonlinear mathematical model to analyze the effects of psychological fear, media-induced awareness, and sanitation practices on bacterial disease dynamics. The model considers infection transmission through direct contacts with infected individuals and indirect exposure to environmental bacteria, assuming bacterial density increases proportional to the infected population. Results show that psychological fear, media-driven awareness, and sanitation play crucial roles in shaping bacterial disease dynamics. A higher growth rate of media advertisements induces limit cycle oscillations in the system via Hopf-bifurcation. However, these oscillations diminish when psychological fear surpasses a threshold. Furthermore, it is found that increasing efficacy of media advertisements in promoting precautionary behaviors and enhancing the depletion rate of bacteria through sanitation efforts by aware individuals can reduce disease prevalence. However, these measures may also induce periodic oscillations by lowering the Hopf-bifurcation threshold for media advertisements growth. An increase in the depletion rate of bacteria due to sanitation efforts can also lead to stability switch via double Hopf-bifurcation, underscoring the need for balanced sanitation strategies to prevent oscillations while ensuring effective disease control. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025.
MODELING THE EFFECTS OF PSYCHOLOGICAL FEAR, TV AND SOCIAL MEDIA ADVERTISEMENTS ON THE CONTROL OF INFECTIOUS DISEASES
(World Scientific, 2025) Maitri Verma; Kuldeep Kumar Tripathi; Arvind Kumar Misra
In this paper, a mathematical model is proposed to study the combined effects of media awareness and fear-induced behavioral changes on the dynamics of infectious diseases. It is considered that in comparison to the unaware individuals, the aware individuals have a lower contact with infected ones. The number of media advertisements is assumed to increase at a rate proportional to the number of infected persons and declines as the number of aware individuals increases. The stability analysis of the model shows that an increase in the growth rate of media advertisements leads to generation of periodic oscillations in the system due to occurrence of Hopf-bifurcation at interior equilibrium. The fear factor and the decline in advertisements due to an increase in the number of aware individuals are found to have stabilizing effect on dynamics of system and their high values can eliminate the limit cycle oscillations present in the system. The rate at which awareness spreads among susceptible individuals and the behavioral response of the aware population are found to be the critical parameters which shape the overall impact of awareness on disease dynamics. It has been observed that the increase in contact rate of aware individuals with infected ones and the dissemination rate of awareness can result into emergence of multiple stability switches via double Hopf-bifurcation. © 2025 World Scientific Publishing Company.
Modeling the impact of mitigation options on abatement of methane emission from livestock
(Lithuanian Association of Nonlinear Analysts, 2017) Arvind Kumar Misra; Maitri Verma
Mitigation of methane emission from livestock sector is crucial to combat the menace of global warming. In the present paper, a nonlinear mathematical model is proposed to investigate the impact of mitigation options for curtailing livestock methane emission on the reduction of atmospheric concentration of methane. In modeling process, it is assumed that the mitigation options are applied at a rate proportion to the livestock population. The conditions for reduction and stabilization of atmospheric methane have been obtained. Numerical simulation has been performed to verify the analytical findings by taking the secondary data of atmospheric concentration of methane, human and livestock populations. Sensitivity analysis is carried out to explore the impact of the key parameters of the model system. © Vilnius University, 2017.
Modeling the impact of mitigation options on methane abatement from rice fields
(Kluwer Academic Publishers, 2014) A.K. Misra; Maitri Verma
The enhanced concentration of methane (CH4) in the atmosphere is significantly responsible for the ominous threat of global warming. Rice (Oryza) paddies are one of the largest anthropogenic sources of atmospheric CH4. Abatement strategies for mitigating CH4 emissions from rice fields offer an avenue to reduce the global atmospheric burden of methane and hence the associated menace of climate change. Projections on population growth suggest that world rice production must increase to meet the population’s food energy demand. In this scenario, those mitigation options are advocated which address both the objectives of methane mitigation and increased production of rice simultaneously. In this paper, we have formulated a nonlinear mathematical model to investigate the effectiveness and limitations of such options in reducing and stabilizing the atmospheric concentration of CH4 while increasing rice yield. In modeling process, it is assumed that implementation rate of mitigation options is proportional to the enhanced concentration of atmospheric CH4 due to rice fields. Model analysis reveals that implementation of mitigation options not always provides “win-win” outcome. Conditions under which these options reduce and stabilize CH4 emission from rice fields have been derived. These conditions are useful in devising strategies for effective abatement of CH4 emission from rice fields along with sustainable increase in rice yield. The analysis also shows that CH4 abatement highly depends on efficiencies of mitigation options to mitigate CH4 emission and improve rice production as well as on the implementation rate of mitigation options. Numerical simulation is carried out to verify theoretical findings. © 2013, Springer Science+Business Media Dordrecht.
Optimal control of anthropogenic carbon dioxide emissions through technological options: a modeling study
(Springer Science and Business Media, LLC, 2018) Maitri Verma; A.K. Misra
The anthropogenic emission of carbon dioxide (CO 2) is the prime culprit for the menace of global warming. To achieve the goal of mitigation of global warming, it is crucial to curb the anthropogenic carbon dioxide emissions. The prime anthropogenic source of CO 2 is fossil fuel burning. In this paper, we propose a nonlinear mathematical model to study the impact of technological options, used for the reduction of CO 2 emissions from fossil fuel burning and industrial processes, on the control of atmospheric CO 2. In the modeling process, it is assumed that the technological options are implemented to curb the CO 2 emissions from the source at a rate proportional to the anthropogenic CO 2 emissions. Model analysis reveals that the atmospheric level of CO 2 can be effectively reduced by increasing the implementation rate of technological options and their efficiency. The strategies which optimally reduce atmospheric CO 2 levels while minimizing the cost associated with the implementation of technological options are identified using optimal control theory. Numerical simulation has been carried out to illustrate theoretical results. © 2016, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.
The Impact of Sea Level Rise Due to Global Warming on the Coastal Population Dynamics: A Modeling Study
(Springer Science and Business Media Deutschland GmbH, 2021) Jang B. Shukla; Maninder S. Arora; Maitri Verma; Arvind K. Misra; Yasuhiro Takeuchi
Global warming and the associated sea level rise is a major environmental issue at present time. The sea level rise is expected to change the demography of the coastal areas due to submergence of land area and thereby cause the migration of population to the inland areas. This paper presents a mathematical model to investigate the effect of global warming and the associated sea level rise on the dynamics of the coastal population. The proposed model is comprised of a set of differential equations which capture the dynamical relationship between seven variables, namely the mass of melting polar ice sheets and glaciers, the seawater level, the land area submerged due to increase in seawater level, the densities of the non-coastal and coastal populations, the carbon dioxide (CO 2) concentration, and the average surface temperature. The model is analyzed qualitatively to study the long-term behavior of the variables of the system. The sufficient conditions under which surface temperature, seawater level, and other model variables settle to the equilibrium levels are derived. The time evolution of surface temperature, seawater level, and coastal population is shown in different carbon dioxide emission scenarios. The sensitivity analysis is carried out to determine the effect of perturbations in the key parameters on the dynamics of the state variables. It is found that the changes in the parameters defining the emission and removal rates of CO 2, and the declination rate of carrying capacity of the coastal population due to an increase in submerged area, significantly influence the coastal population dynamics. The study suggests that the policies aiming to limit the impact of sea level rise on coastal population must focus on mitigation of carbon dioxide emissions. © 2021, King Abdulaziz University and Springer Nature Switzerland AG.