Browsing by Author "Arvind Kumar Misra"

Now showing 1 - 20 of 69

A COMPREHENSIVE INVESTIGATION INTO DETERMINISTIC AND STOCHASTIC MODELS CONCERNING THE EFFECTS OF SEEDING ON RAINFALL AND ATMOSPHERIC POLLUTION
(World Scientific, 2025) Amita Tripathi; Sayan Mandal; Pankaj Kumar Tiwari; Arvind Kumar Misra; Maia Martcheva
This study introduces a mathematical model aimed at evaluating the potential influence of aerosol introduction into the atmosphere for inducing rainfall and managing atmospheric pollution. By expanding on the proposed model, we incorporate stochastic elements to encompass environmental white noises that impact the system’s dynamics. Both mathematical and numerical methods are employed to analyze the system’s behavior. In the context of the deterministic model, we examine the solutions’ positivity and boundedness, identify feasible equilibria, and scrutinize the stability characteristics both locally and globally. The analysis of the stochastic system encompasses discussions regarding the existence of a unique solution, its ultimate boundedness, and the conditions that prompt the establishment of a unique stationary distribution characterized by ergodic properties. Our simulations illustrate that augmenting cloud formation rates and externally introduced aerosols can amplify rainfall while mitigating atmospheric pollution levels. Minor intensities of white noise do not alter the system’s behavior, whereas significant intensities result in high-amplitude oscillations of the system’s variables. We explore the effects of white noise intensities using histograms and stationary distributions, highlighting long-term rainfall trends in a noisy environment. © 2025 World Scientific Publishing Company.
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 dynamical study to combat atmospheric pollutants using aerial water spray and sustain industrialization
(American Institute of Physics, 2025) Gauri Agrawal; Arvind Kumar Misra
In pursuit of global development and civilization, the accelerated pace of industrialization has brought significant atmospheric challenges, posing serious risks to public health. This study examines the implications of industrial establishment and relocation/closure, focusing on the emission of atmospheric pollution, all associated with the human population. To capture the interwoven dynamics, a novel three-dimensional nonlinear mathematical model is formulated. Bifurcation analysis of the model reveals complex dynamical behaviors, including the emergence of transcritical, saddle-node, subcritical, and supercritical Hopf bifurcations. Critical thresholds are identified for the establishment rate (and the relocation/closure rate) of industries, beyond which the system loses (and gains) its stability. To overcome with the industrial and anthropogenic atmospheric pollution, the model system is extended by introducing a new dynamic variable representing aerial water spraying as a pollution removal technique. The extended system significantly suppresses bifurcations, terminates limit cycle oscillations, and promotes asymptotic stability. Further findings reveal that increasing the water spraying rate reduces the concentration of atmospheric pollutants and simultaneously increases the densities of human population and industries. The system’s stability region expands as the spraying rate increases, along with the increasing industrial establishment rate. Also, the concentration of atmospheric pollutants attains a minimum when both the aerial water spraying rate and the scavenging rate of atmospheric pollution through aerial water spraying are maximized. The study further identifies an optimal control strategy for aerial water spraying that minimizes the atmospheric pollutants at the lowest possible cost. © 2025 Author(s).
A fractional model for insect management in agricultural fields utilizing biological control
(Springer Science and Business Media Deutschland GmbH, 2025) Arvind Kumar Misra; Akash Yadav; Ebenezer Bonyah
Bio-insecticides, such as baculoviruses, are the most well-known and environment friendly alternative to chemical insecticides in agriculture. In this research work, our main goal is to develop a sustainable and effective approach to control insect population by using the potential of baculoviruses. To achieve this, we formulate a novel fractional-order model utilizing the Caputo fractional operator to meticulously analyze the effects of baculovirus as a biological insecticide on insect population and consequently on crop yield. Since the virus density depletes rapidly due to ultraviolet (UV) radiation, enzymatic attacks, temperature variations and other factors in the crop field, a one-time spray of bio-insecticide may not be effective in controlling insects within a sufficient time frame. Therefore, we posit that the spraying of baculovirus is proportional to the density of the susceptible insects. The dynamic behavior of the baculovirus model underscores the critical influence of the fractional-order derivative in shaping the system’s behavior and stability. Additionally, the model analysis brings to light the intricate interplay between virus replication rate and virus infection rate in regulating insect density. To further enhance the model’s applicability, we also propose a fractional optimal control strategy to effectively reduce the insect density and associated costs, taking into account the time-dependent spraying rate of the virus. Numerical results obtained using the Adams–Bashforth–Moulton method, corroborate our analytical insights and underscore the importance of fractional-order derivative in this context. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
A fuzzy graph-theoretic approach to quantify the effect of skill acquisition on unemployment
(Elsevier B.V., 2025) Ashutosh Upadhayay; Jyoti P. Maurya; Arvind Kumar Misra
Unemployment remains a critical global challenge, particularly in developing economies, where the gap between job seekers' skills and employer demands continues to widen. Building on the work of Misra et al. [1], who used a crisp graph-theoretic approach to model workforce transitions, this study introduces a fuzzy graph-theoretic framework to better capture uncertainties and gradations in real-world employment dynamics. Unlike traditional binary models, this approach incorporates varying degrees of influence, strength, and uncertainty in social connections, enabling a more nuanced representation of transitions between employment states. A key contribution of this study is the derivation of fuzzy reproduction number (R˜0f), which serves as a threshold for the spread of employment opportunities. When R˜0f<1, unskilled unemployment persists due to weak transitions, while R˜0f>1 leads to the dominance of the skilled population. At the critical threshold R˜0f=1, the model demonstrates that individuals eventually transition to either skilled unemployed or employed states, with the possibility that the entire population may achieve full employment. Numerical simulations validate these findings, showing that under weak conditions, unskilled unemployed individuals dominate, whereas favorable conditions result to skilled employed individuals' dominance. The adaptive weight mechanism dynamically updates the connection strengths, modeling the natural tendency to strengthen ties with similarly employed individuals. © 2025 Elsevier B.V.
A Mathematical Model for the Effects of Nitrogen and Phosphorus on Algal Blooms
(World Scientific Publishing Co. Pte Ltd, 2019) Pankaj Kumar Tiwari; Sudip Samanta; Jocirei D. Ferreira; Arvind Kumar Misra
The increase of nutrients in lakes typically stimulates the growth of algae in this environment. Therefore, it is important to understand the connection between nutrient concentration and algal biomass to manage the water pollution caused by excessive plant nutrients. It is worth observing that phosphorus and nitrogen are often considered as the principal limiting nutrients for aquatic algal production due to their short supply compared to cellular growth requirements. In freshwaters, phosphorus is the least abundant among the nutrients needed in large quantity by photosynthetic organisms, hence this is the primary nutrient that limits their growth. The purpose of this work is to compare the effects of nitrogen and phosphorus on the growth of algae in lakes. By using a sensitivity analysis technique, we found that the sources of phosphorus provide a greater risk for bloom of algae than that of nitrogen. Therefore, to reduce the occurrence of algal bloom more attention should be paid for the control of phosphorus input into the lake but the inflow of nitrogen cannot be ignored. The existence of a transcritical bifurcation is discussed and its direction is investigated by applying the projection method technique. Further, to make the system more realistic, time delay involved in the conversion of detritus into nutrients is considered. We show that for increasing values of time delay, the system undergoes an Andronov-Hopf-bifurcation. Some simulations are presented to verify the analytical findings. The results of our study can be helpful for the policy makers to mitigate algal blooms from lakes. © 2019 World Scientific Publishing Company.
A mathematical model for the impact of disinfectants on the control of bacterial diseases
(Taylor and Francis Ltd., 2023) Rabindra Kumar Gupta; Rajanish Kumar Rai; Pankaj Kumar Tiwari; Arvind Kumar Misra; Maia Martcheva
Here, we investigate a mathematical model to assess the impact of disinfectants in controlling diseases that spread in the population via direct contacts with the infected persons and also due to bacteria present in the environment. We find that the disease-free and endemic equilibria of the system are related via a transcritical bifurcation whose direction is forward. Our numerical results show that controlling the transmissions of disease through direct contacts and bacteria present in the environment can help in reducing the disease prevalence. Moreover, fostering the recovery rate and the death rate of bacteria play significant roles in disease eradication. Our numerical observations convey that reducing the bacterial density at the source discharged by the infected population through the use of chemicals has prominent effect in disease control. Overall, our findings manifest that the disinfectants of high quality can completely control the bacterial density and the disease outbreak. © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
A mathematical model to restore water quality in urban lakes using phoslock
(American Institute of Mathematical Sciences, 2021) Pankaj Kumar Tiwari; Rajesh Kumar Singh; Subhas Khajanchi; Yun Kang; Arvind Kumar Misra
Urban lakes are the life lines for the population residing in the city. Excessive amounts of phosphate entering water courses through household discharges is one of the main causes of deterioration of water quality in these lakes because of the way it drives algal productivity and undesirable changes in the balance of aquatic life. The ability to remove biologically available phosphorus in a lake is therefore a major step towards improving water quality. By removing phosphate from the water column using Phoslock essentially deprives algae and its proliferation. In view of this, we develop a mathematical model to investigate whether the application of Phoslock would significantly reduce the bio-availability of phosphate in the water column. We consider phosphorus, algae, detritus and Phoslock as dynamical variables. In the modeling process, the introduction rate of Phoslock is assumed to be proportional to the concentration of phosphorus in the lake. Further, we consider a discrete time delay which accounts for the time lag involved in the application of Phoslock. Moreover, we investigate behavior of the system by assuming the application rate of Phoslock as a periodic function of time. Our results evoke that Phoslock essentially reduces the concentration of phosphorus and density of algae, and plays crucial role in restoring the quality of water in urban lakes. We observe that for the gradual increase in the magnitude of the delay involved in application of Phoslock, the autonomous system develops limit cycle oscillations through a Hopf-bifurcation while the corresponding nonautonomous system shows chaotic dynamics through quasi-periodic oscillations. © 2021 American Institute of Mathematical Sciences. All rights reserved.
A nonautonomous mathematical model to assess the impact of algae on the abatement of atmospheric carbon dioxide
(World Scientific, 2021) Pankaj Kumar Tiwari; Rajesh Kumar Singh; Debaldev Jana; Yun Kang; Arvind Kumar Misra
The world's oceans have played an important role in sequestering atmospheric carbon dioxide through solubility and the action of algae. Fixation of atmospheric carbon dioxide by photoautotrophic algal cultures has the potential to diminish the release of carbon dioxide into the atmosphere, thereby helping to alleviate the trend toward global warming. This work investigates the role of algae in controlling the level of atmospheric carbon dioxide. Partial Rank Correlation Coefficients (PRCCs) technique is used to address how the concentration of atmospheric carbon dioxide is affected by changes in a specific parameter disregarding the uncertainty over the rest of the model parameters. Parameters related to algal growth are shown to significantly reduce the level of atmospheric CO2. Further, we explore the dynamics of nonautonomous system by incorporating the seasonal variations of some ecologically important model parameters. Our nonautonomous system exhibits globally attractive positive periodic solution, and also the appearance of double periodic solution is observed. Moreover, by letting the seasonally forced parameters as almost periodic functions of time, we show almost periodic behavior of the system. Our findings suggest that the policy makers should focus on continuous addition of nutrients in the ocean to accelerate the algal growth thereby reducing the level of carbon dioxide in the atmosphere. © 2021 World Scientific Publishing Company.
A simple mathematical model for the spread of two political parties
(Vilnius University Press, 2012) Arvind Kumar Misra
In this paper, a non-linear mathematical model for the spread of two political parties has been proposed and analyzed by using epidemiological approach. The whole population is assumed to be a constant and homogeneously mixed. Equilibria have been obtained analytically and their local and global stability have been discussed. Conditions for the co-existence of both the political parties have been obtained. Numerical simulation is also performed to support the analytical results. © Vilnius University, 2012.
An Efficient Fluorescent Probe Based on Triphenylimidazole End-Capped Diketopyrrolopyrrole for Selective Detection of CN− and TFA Through On–Off–On Response
(John Wiley and Sons Ltd, 2025) Arvind Kumar Misra; Rimpi Bhandari; Mohammed Kaleem; Ravisen Rai; Tripathi Shivam Saroj Kumar
A triphenyl-imidazole end-capped donor–acceptor type potential molecular probe 3 has been designed and synthesized. Probe 3 upon interaction with different classes of metal ions/anions and NPPs displayed high selectivity with CN− anion (LOD = 20.42 nM) through fluorescence “turn-Off” response and a naked-eye sensitive visible color change. Job's plot analysis revealed a 1:2 binding stoichiometry. The interaction of 3.CN− with trifluoroacetic acid (TFA) showed reversible behavior wherein the intensity of the probe rejuvenated, fluorescence “turn On-Off-On response,” along with a change in color of the medium. The change in rate constants and fluorescence lifetime of the probe suggested that the interaction of probe with CN− occurred in two steps: H-binding and deprotonation of –NH functions of imidazolyl units. The mode of binding of probe with CN− was confirmed by 1H NMR, FTIR, and HRMS data. The potential application of molecular probe has been examined to detect the CN−, TFA, and TFA vapor on test paper strips. The smartphone-based RGB analysis of paper strips also supported on-site colorimetric detection of CN−. Probe shows good recovery percentage of CN− in real water sample analysis. The output emission using chemical inputs CN− and TFA mimics the function of an IMP logic gate. © 2025 John Wiley & Sons Ltd.
An optimal control model for cloud seeding in a deterministic and stochastic environment
(John Wiley and Sons Ltd, 2020) Arvind Kumar Misra; Amita Tripathi
To promote artificial rain in India and other such developing countries, in this article, we have proposed and analyzed a nonlinear mathematical model for cloud seeding by considering that aerosols are introduced proportional to the density of water vapors present in the atmosphere. The model is analyzed using Lyapunov's stability theory of differential equations. To reduce the cost of cloud seeding, an optimal control strategy is designed by incorporating four control parameters. We have shown the existence and uniqueness of solution of this optimal control problem, using Pontryagins Maximum Principle. To minimize the cost in making artificial rain, the optimal control problem provides the strategy for the rate of introduction of aerosols in the atmosphere. To capture the effects of environmental noise on control strategies, the model in deterministic framework is converted into stochastic framework. In this regard, the Hamilton-Jacobi-Bellman equation for stochastic control cost function has been formed. The stochastic analysis implies that the control strategy is effective in reducing the cost and increasing rainfall. © 2020 John Wiley & Sons, Ltd.
AN OPTIMAL CONTROL MODEL FOR THE IMPACT OF PHOSLOCK ON THE MITIGATION OF ALGAL BIOMASS IN LAKES
(World Scientific, 2022) Pankaj Kumar Tiwari; Subarna Roy; Grant Douglas; Arvind Kumar Misra
In this study, we investigate the effects of excessive inputs of bioavailable phosphorus into a lake from agricultural fields and households on algal bloom formation, and its potential management by using the lanthanum-modified clay Phoslock as a bioavailable phosphorus adsorbent. We also investigate the impact of time delay involved in the process of applying Phoslock after measuring the density of algal biomass in the lake. Moreover, the seasonal effects in the input of bioavailable phosphorus from the agricultural lands and the application rate of Phoslock have been investigated. Our simulation results show that the algal growth accelerates if the bioavailable phosphorus is excessively loaded through agricultural runoff and domestic discharges. However, algal biomass can be effectively controlled by employing Phoslock in a sufficiently large quantity. Further, we find that a delay in the application of Phoslock induces limit cycle oscillations. Furthermore, our findings show that the combined actions of delay and periodicity in the application of Phoslock bring forth dynamical complexity in the lake system by giving rise to higher periodic solutions and bursting patterns. Lastly, we investigate an optimal control problem to estimate the optimum dosage of Phoslock for the mitigation of algal biomass from the lake system. © 2022 World Scientific Publishing Company.
Analysis of a delayed MISCR rumor spread model with refutation mechanism
(Springer Science and Business Media Deutschland GmbH, 2024) Moumita Ghosh; Arvind Kumar Misra; Pritha Das
The sustainability of the social order is chasing the severe challenge of increasing the spread of rumors on social media. The popularity of social media platforms is disastrously contributing to the spread of harmful rumors, posing a threat to society. In this article, we have formulated MISCR model by incorporating mainstream media to a social media population containing ignorant, spreader, counter-rumor spreader and stifler. In addition, a time delay is introduced in the transformation process of ignorant individuals after interaction with counter-rumor spreaders. First, the qualitative behaviors of the corresponding non-delayed system are studied, followed by the derivation of the spreading threshold of rumor (R0). Subsequently, sensitivity of R0 with respect to input parameters is studied using normalized forward sensitivity analysis. To illustrate the impact of delay on rumor propagation existence conditions of Hopf and Hopf–Hopf bifurcations have been analyzed. Also, sufficient conditions for Hopf bifurcation regarding the interference of counter-rumor spreaders are determined. Subsequently, some numerical simulations are demonstrated to validate the analytical results. Moreover, some complex phenomena like stability switch, chaos are observed numerically. It is also found that the governmental input in refutation mechanism can effectively remove the chaos. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024.
Analyzing the Synergistic Effects of Population and Pollution on Forest Resources: A Mathematical Model
(World Scientific, 2025) Anjali Jha; Arvind Kumar Misra
The alteration in concentration of atmospheric pollutants is influencing the functionality and growth of forests. Also, the growing human demand for forestry resources is detrimentally affecting the sustainability of these valuable resources. In this study, we present a mathematical model that incorporates the influence of atmospheric pollutants on the intrinsic growth rate of forests, while concurrently addressing the utilization of forestry land by the human population for diverse purposes which diminishes the carrying capacity of forestry resources. We establish sufficient conditions under which all relevant dynamic variables stabilize at their equilibria. Upon scrutinizing the model system, we observe multiple bifurcations concerning certain key parameters. Additionally, numerical simulations have been conducted to corroborate the analytically derived findings. Moreover, we fortify the proposed model through the integration of a time delay in the impact of pollutants on the intrinsic growth rate of forestry resources. Despite the conventional belief that introducing a time delay tends to destabilize systems, our resolute delayed model system showcases that a time delay in the effect of pollutants on intrinsic growth rate of forestry resources can, in fact, stabilize the unstable interior equilibrium. © 2025 World Scientific Publishing Company.
Assessing the multifaceted repercussions of chemical insecticides on vegetable yield and human population: A modeling study
(Elsevier Inc., 2025) Akash Yadav; Arvind Kumar Misra
Vegetables stand out as invaluable reservoirs of essential vitamins, minerals, antioxidants, and vital dietary elements, yet their production faces a considerable threat due to insects. To tackle this challenge, farmers spray chemical insecticides to enhance vegetable yields by controlling the insect population. Nevertheless, the presence of insecticide residues in vegetables stands as a primary contributor to acute illnesses and chronic health conditions in humans. In the present research work, we formulate a novel nonlinear mathematical model meticulously designed to scrutinize the multifaceted repercussions of chemical insecticides on vegetable yield and the human population. In our model formulation, we adopt a dynamic approach where insecticide application on vegetables in agricultural fields correlates with the insect population. However, we acknowledge the consequential impact of insecticide usage on human health, which in turn reduces the growth rate of the human population. This study determines the critical value of the spraying rate of insecticide at which the human population reaches its maximum, ensuring that human needs for vegetables are met while minimizing the adverse effects of insecticide. Since various species of insects attack vegetables in the field and different insect species have different natural mortality rates, therefore we also identify the range of natural mortality rates of insects for which vegetable yield is minimal and fluctuates with time. Further, our research reveals that if the natural mortality rate of insects in a certain crop field lies within this identified range, then farmers should increase the insecticide spraying rate to avoid this upheaval situation and stabilize vegetable yield at a higher level. © 2024 Elsevier Inc.
Bifurcation analysis of fish-algae-nutrient interactions in aquatic ecosystems
(Springer Science and Business Media B.V., 2025) Jyoti P. Maurya; Arvind Kumar Misra; Santo N. Banerjee
The overgrowth of algae in lakes often stems from an influx of nutrients from various sources, such as run-off from agricultural areas, anthropogenic and industrial drainage. Phosphorus and nitrogen play a crucial role as catalysts for algae growth, driving their rapid proliferation and leading to the formation of algal blooms. Both herbivorous and carnivorous fish play vital roles in the aquatic food web, and their presence can significantly affect the dynamics of algae within the aquatic ecosystem. Thus, a mathematical model is proposed to investigate the influence of fish on algae-nutrient interactions. For the model formulation, herbivorous fish are considered to depend on algae as their primary food source, while carnivorous fish rely on herbivorous fish for their survival and growth. Our analytical results confirm the existence of one parametric bifurcation, including saddle-node and Hopf bifurcations. Additionally, when the model is transformed into discrete-time intervals, it undergoes a Neimark-Sacker bifurcation. The existence of one parametric bifurcation is shown by considering the maximum uptake rate of nutrients by algae as a bifurcation parameter. Numerical simulations further demonstrate that the proposed model system exhibits two-parametric bifurcations, such as cusp, Bogdanov-Takens, generalized Hopf, Chenciner, and zero-Hopf bifurcations. The basin of stability is used to assess how the initial conditions and parameter values influence the bistability of the proposed mathematical model. This comprehensive analysis of algae-nutrient-fish interactions provides valuable insights into the complex dynamics of aquatic ecosystems, offering a foundation for better understanding and potentially managing algal blooms in aquatic ecosystem. © The Author(s), under exclusive licence to Springer Nature B.V. 2024.
CHAOTIC DYNAMICS of A STAGE-STRUCTURED PREY-PREDATOR SYSTEM with HUNTING COOPERATION and FEAR in PRESENCE of TWO DISCRETE DELAYS
(World Scientific, 2023) Soumitra Pal; Ashvini Gupta; Arvind Kumar Misra; Balram Dubey
Depending on behavioral differences, reproductive capability and dependency, the life span of a species is divided mainly into two classes, namely immature and mature. In this paper, we have studied the dynamics of a predator-prey system considering stage structure in prey and the effect of predator-induced fear with two discrete time delays: maturation delay and fear response delay. We consider that predators cooperate during hunting of mature prey and also include its impact in fear term. The conditions for existence of different equilibria, their stability analysis are carried out for non-delayed system and bifurcation results are presented extensively. It is observed that the fear parameter has stabilizing effect whereas the cooperative hunting factor having destabilizing effect on the system via occurrence of supercritical Hopf-bifurcation. Further, we observe that the system exhibits backward bifurcation between interior equilibrium and predator free equilibrium and hence the situation of bi-stability occurs in the system. Thereafter, we differentiate the region of stability and instability in bi-parametric space. We have also studied the system's dynamics with respect to maturation and fear response delay and observed that they also play a vital role in the system stability and occurrence of Hopf-bifurcation is shown with respect to both time delays. The system shows stability switching phenomenon and even higher values of fear response delay leads the system to enter in chaotic regime. The role of fear factor in switching phenomenon is discussed. Comprehensive numerical simulation and graphical presentation are carried out using MATLAB and MATCONT. © 2023 World Scientific Publishing Company.
Combating unemployment through skill development
(Vilnius University Press, 2020) Arvind Kumar Singh; Pushkar Kumar Singh; Arvind Kumar Misra
In this paper, we propose and analyze a nonlinear mathematical model to study the effect of skill development on unemployment. We assume that government promulgates different levels of skill development programs for unemployed persons through which two different categories of skilled persons, namely, the low-skilled and the highly-skilled persons, are coming out and the highly-skilled persons are able to create vacancies. The model is studied using stability theory of nonlinear differential equations. We find analytically that there exists a unique positive equilibrium point of the proposed model system under some conditions. Also, the resulting equilibrium is locally as well as globally stable under certain conditions. The effective use of implemented policies to control unemployment by providing skills to unemployed persons and the new vacancies created by highly-skilled persons are identified by using optimal control analysis. Finally, numerical simulation is carried out to support analytical findings. © 2020 Authors. Published by Vilnius University Press.
Delay in budget allocation for vaccination and awareness induces chaos in an infectious disease model
(Taylor and Francis Ltd., 2021) Arvind Kumar Misra; Rajanish Kumar Rai; Pankaj Kumar Tiwari; Maia Martcheva
In this paper, we propose a model to assess the impacts of budget allocation for vaccination and awareness programs on the dynamics of infectious diseases. The budget allocation is assumed to follow logistic growth, and its per capita growth rate increases proportional to disease prevalence. An increment in per-capita growth rate of budget allocation due to increase in infected individuals after a threshold value leads to onset of limit cycle oscillations. Our results reveal that the epidemic potential can be reduced or even disease can be eradicated through vaccination of high quality and/or continuous propagation of awareness among the people in endemic zones. We extend the proposed model by incorporating a discrete time delay in the increment of budget allocation due to infected population in the region. We observe that multiple stability switches occur and the system becomes chaotic on gradual increase in the value of time delay. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.