2025
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PublicationArticle 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. BanerjeeThe 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.PublicationArticle Assessing the multifaceted repercussions of chemical insecticides on vegetable yield and human population: A modeling study(Elsevier Inc., 2025) Akash Yadav; Arvind Kumar MisraVegetables 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.PublicationArticle Analyzing the Synergistic Effects of Population and Pollution on Forest Resources: A Mathematical Model(World Scientific, 2025) Anjali Jha; Arvind Kumar MisraThe 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.PublicationArticle Modeling the effect of temperature rise due to atmospheric carbon dioxide on the outbreak of food-borne diseases(Springer Nature, 2025) Shikha Singh; Shubham Chaudhry; Maninder Singh Arora; Rajeev Kumar Singh; Arvind Kumar MisraClimate change is not just a future concern but it is a present reality. As atmospheric carbon dioxide levels in the atmosphere increase, global temperature rises, triggering a series of environmental changes. One of the less-discussed but significant impact is the spread of food-borne diseases. This article delves into how rising temperature influences food safety. Temperature rise affects the growth and survival of pathogens and warmer temperature can accelerate the replication rate of bacteria and other microorganisms, increasing the likelihood of infection. Furthermore, higher temperature can also affect the life cycles of vectors, enhancing their ability to spread diseases. A non-linear model is presented and examined in this study to investigate the impact of rising global average temperature on the transmission of carrier-dependent infectious diseases within a specific habitat. The model incorporates five dynamic variables: carbon dioxide concentration, global average temperature, susceptible and infected human population, and carrier population density. We assume that the carrier population follows a logistic growth model with temperature-dependent intrinsic growth rate and carrying capacity. The analysis demonstrates that as global temperature rise, there is an observed increase in both the density of carriers and the number of infected individuals within population. Reducing anthropogenic carbon dioxide emissions may help in controlling the transmission of infectious diseases reliant upon carriers. Numerical simulations, using appropriate parameter values, confirm analytical findings. © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2025.PublicationArticle Modeling the effect of fear-inducing awareness programs on smoking cessation(Elsevier B.V., 2025) Jyoti P. Maurya; Mamta Kumari; Arvind Kumar MisraSmoking remains a significant public health challenge, contributing to numerous preventable diseases and mortality worldwide. Addressing this issue requires innovative strategies to enhance smoking cessation rate. In this research work, we develop a mathematical model to evaluate the impact of fear-inducing awareness programs on promoting smoking cessation. The model incorporates the parameters depicting the behavioral changes of individuals to capture the dynamic interplay between fear-driven awareness programs and smoking behavior. We analyze the local and global stability of the equilibria obtained from the model, providing a comprehensive understanding of the system's dynamics. Furthermore, we identify critical bifurcation phenomena, including saddle–node and transcritical bifurcations, occurring in both forward and backward directions, which elucidate the system's qualitative changes under parameter variations. Numerical simulations are conducted using smoking prevalence data from the United States of America (USA) to validate the analytical results and explore the influence of key parameters on smoking behavior. Our findings highlight that intensifying the fear component within awareness programs is more effective in promoting smoking cessation compared to merely increasing the number of such programs. © 2025PublicationArticle Modeling the consequences of elevated temperature on crop yield and insect population: a bifurcation and seasonal analysis(Springer Science and Business Media B.V., 2025) Anjali Jha; Akash Yadav; Arvind Kumar MisraHuman-induced climate change is impacting regions worldwide, with agriculture being particularly vulnerable. The increase in carbon dioxide (CO2) emissions is driving significant challenges, including global warming, rising sea levels, drought and frequent insect outbreaks. While moderate increase in CO2 and temperature may initially boost crop growth, exceeding critical threshold can disrupt photosynthesis and reduce leaf area and longevity, impairing productivity. This research work presents a novel mathematical model to explore the effects of elevated CO2 and temperature on crop yield and insect population dynamics. Our model assumes that rising CO2 levels increase surface temperature, which initially promote crop growth but eventually lead to a decline, once a critical temperature threshold is surpassed. Additionally, higher temperature accelerates insect population growth, which negatively impacts crop production. Model analysis reveals several bifurcations in the system. Further, by incorporating seasonal variations, we perform a comprehensive mathematical and numerical analysis of the associated nonautonomous system. Our analysis uncovers periodic solutions when the autonomous system is stable, and complex dynamics, including higher-period oscillations and chaos, when the autonomous system exhibits limit cycle oscillations. This study provides insights into the intricate interplay between CO2 level, global average temperature, insect population and crop yield, offering potential strategies to safeguard agricultural productivity in the face of climate change. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.PublicationArticle Impact of Human Activities and Forest Biomass on Atmospheric Carbon Dioxide: A Mathematical Model(Springer Science and Business Media Deutschland GmbH, 2025) David Mbelle Ngoh; Anjali Jha; Bring; Arvind Kumar Misra; Dany Pascal Moualeu Ngangue; Louis Aimé FonoThe primary driving force for the impending threat of global warming is the heightened concentration of carbon dioxide (CO2) in the atmosphere. In this research work, a mathematical model has been developed to investigate the impact of both human activities and forest biomass on the dynamics of atmospheric carbon dioxide. This model assumes that the concentration of CO2 in the atmosphere rises due to a combination of natural processes and human activities. Additionally, it posits that forest biomass and other natural sinks absorb atmospheric CO2. The equilibria of the model have been determined, and their stability has been thoroughly examined. The analysis of the model reveals that an escalation in thermal plants or industries corresponds to a rise in atmospheric level of CO2. Notably, the model analysis identifies that the deforestation rate either due to thermal plants or industries or both has destabilizing effects on the system’s dynamics, i.e., if these parameters surpass a certain threshold, the system loses its stability, potentially giving rise to periodic solutions through Hopf bifurcation. Also, it is found that transcritical bifurcation takes place between interior and forest biomass-free equilibria as the deforestation either due to industrial activities or thermal plants related activities increases. To validate the theoretical findings, numerical simulations have been conducted, providing additional support to the analytical findings and their future implications. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.