2025

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Modeling the impact of temperature on the dynamics of carrier-dependent infectious diseases with control strategies
(American Institute of Mathematical Sciences, 2025) Shubham Chaudhry; Gauri Agrawal; Maia Martcheva; Arvind Kumar Misra
The spread of diseases poses significant threats to human health globally. The dynamic nature of infectious diseases, especially those that also rely on carriers (e.g., house flies) for transmission, requires innovative strategies to control their spread, as environmental conditions such as temperature, humidity, etc., affect the rate of growth of the carrier population. This study introduces a mathematical model to assess the effect of increasing global average temperature rise caused by carbon dioxide emissions and chemical control strategies on the dynamics of such diseases. The stability properties of feasible equilibrium solutions were discussed. Sensitivity analysis was also performed to highlight the key parameters that may help to design effective intervention strategies to control disease transmission. The model was further analyzed for an optimal control problem by incorporating a control measure on the application rate of chemical insecticides to reduce the carrier population. Through the combination of analytical techniques and numerical simulations, we have evaluated the effectiveness of chemical control strategies under varying epidemiological parameters. The model also explored the critical thresholds necessary for achieving disease control and eradication. Our results are valuable to public health officials and policymakers in designing effective interventions against carrier-dependent infectious diseases. © 2025 the Author(s), licensee AIMS Press.
Modeling the impact of air and water pollutants emitted from industries on rainfall
(World Scientific, 2025) Gauri Agrawal; Alok Kumar Agrawal; Arvind Kumar Misra
Rainfall regulates the hydrological cycle on the planet Earth, sustains our ecological system, and provides fresh water to all living beings. In the recent past, a deterioration in rainfall has been observed due to the increased level of pollutants emitted by industries in the environment. The presence of these industrial pollutants in the environment affects the processes of evaporation, condensation, and nucleation, requisite in forming cloud droplets and raindrops. In formulating the model, we categorize the total emissions of industrial pollutants into surface water pollutants and atmospheric pollutants in the environment to assess their effect explicitly on rainfall. We presume the natural formation rate of cloud droplets as a decreasing function of surface water pollutants. It is further assumed that the density of cloud droplets decreases due to atmospheric pollutants; and the surface water pollutants in regional water bodies increase due to the leaching of atmospheric pollutants during rainfall. To analyze the formulated model system, we use the qualitative theory of differential equations. The equilibrium solution is obtained, and its stability properties are discussed. The numerical analysis is performed to substantiate the analytically obtained results of the formulated mathematical model. The obtained results clearly show that industrial pollutants emitted into the environment exert a negative impact on rainfall. © 2025 World Scientific Publishing Company.
Modeling the Effect of Contractual Jobs on Unemployment With a Case Study of the Indian Agnipath Scheme
(John Wiley and Sons Ltd, 2025) Arvind Kumar Misra; Mamta Kumari; Dayaram Sahu
Contractual employment offers a relevant avenue for reducing the unemployment period within a labor force. Additionally, they offer valuable work experience to individuals, thereby enhancing their chances of securing regular employment. In this article, we introduce a four-dimensional stage-structured model, taking the service period of contractual jobs as a delay parameter. This approach enables us to examine the impact of contractual employment on the dynamics of unemployment. The proposed model is examined using the stability theory of delay differential equations, revealing that the system has a unique equilibrium that is globally stable under certain conditions for any value of the delay parameter. Furthermore, we analytically derive specific conditions under which an increase in the contractual job tenure either increases or decreases unemployment. Additionally, we validate our analytical findings numerically by using India's unemployment-employment data and considering the employment opportunities provided under the Indian Agnipath scheme as an illustrative example of contractual employment. © 2025 John Wiley & Sons Ltd.
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.
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.
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.
Modeling the impacts of chemical substances and time delay to mitigate regional atmospheric pollutants and enhance rainfall
(Elsevier B.V., 2025) Gauri Agrawal; Alok Kumar Agrawal; Arvind Kumar Misra
Rainfall, a crucial process of the hydrological cycle, involves the condensation of atmospheric cloud droplets into raindrops that fall on the Earth's surface, providing essentials for human well-being and ecosystem. Research studies show that the condensation–nucleation process for forming raindrops is reduced due to atmospheric pollutants. In this scenario, introducing chemical substances may effectively mitigate regional atmospheric pollution, and reduced atmospheric pollution may lead to adequate rainfall. In the present research work, we analyze rainfall dynamics using a modeling approach with the incorporation of a time lag involved between measuring the data for atmospheric pollution and introducing chemical substances in the regional atmosphere. Here, we assume the formation rate of cloud droplets as a decreasing function of atmospheric pollutants. It is also assumed that introducing chemical substances reduces regional atmospheric pollution. Involving time delay as a bifurcation parameter, we analyze the stability, direction, and period of the bifurcating periodic solutions arising through Hopf bifurcation. Along with this, the presented numerical simulations corroborate the analytical results of our mathematical model. The modeling study reveals that the use of chemical substances in proportion to the concentration of atmospheric pollutants measured at time (t−τ) becomes crucial to mitigate the atmospheric pollutants because as time delay exceeds a threshold value, the system loses its stability and undergoes Hopf bifurcation. © 2025 Elsevier B.V.
Graph-theoretic approach and bifurcation analysis of skill acquisition and its effect on unemployment
(American Institute of Physics, 2025) Arvind Kumar Misra; Ashutosh Upadhayay; Mamta Kumari; Jyoti P. Maurya
In developing countries, the informal sector plays a crucial role in employing unskilled labor workforce and contributes significantly to economic growth. Informal sector also facilitates skill acquisition, which enhances workers’ employability. This research work presents a dynamical model examining how skilled individuals in the informal sector influence unemployment dynamics. The model considers unemployed persons (both unskilled and skilled) and employed persons as dynamic variables. We analyze the feasibility and stability of all equilibria for the proposed dynamical system. A quantity R 0 , analogous to the basic reproductive ratio in epidemic models, is derived. We also demonstrate the existence of various bifurcations, including transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations. Additionally, we apply a graph-theoretical approach to analyze unemployment patterns and connections within the labor workforce. This provides insights into the structure and dynamics of unemployment networks, complementing the dynamical system’s analysis. By combining dynamical system’s theory with graph theory, this study provides a comprehensive, multi-dimensional understanding of unemployment dynamics in developing economies characterized by substantial informal sector. © 2025 Author(s).
Role of awareness programs on diabetes prevention and control of viral infection: a study of optimal control
(Springer Science and Business Media Deutschland GmbH, 2025) Kalyan Kumar Pal; Rajanish Kumar Rai; Pankaj Kumar Tiwari; Arvind Kumar Misra
Diabetes is a chronic metabolic disorder characterized by elevated blood glucose levels due to insufficient insulin production or ineffective use of insulin. While primarily driven by genetics and lifestyle, viral infections like enteroviruses, cytomegalovirus, hepatitis C, HIV, and COVID-19 have also been linked to triggering both type 1 and type 2 diabetes (T2D), possibly through immune system-induced metabolic changes. In this study, we propose and analyze a nonlinear mathematical model to investigate the effects of awareness campaigns on diabetes prevention and control of viral infection. We assume that individuals who are initially unaware of diabetes risk factors become informed through word-of-mouth communication, and adopt preventive behaviors. The model also includes the impact of social media and television advertisements in raising public awareness. We derive the basic reproduction number (R0) for the system, which serves as a threshold parameter. Our analysis indicates that the system experiences a transcritical bifurcation as R0 crosses the unit value, indicating a shift in the stability of equilibria, and the potential for diabetes control. Additionally, we conduct a sensitivity analysis to identify the most influential parameters impacting the number of infected cases. The model is further expanded to incorporate two control strategies aimed at reducing the prevalence of both diabetic and at-risk individuals. Pontryagin’s Maximum principle, along with the forward-backward sweep method, is employed to solve the optimal control problem. Our findings evoke that interventions involving social media and television advertisements are more effective in promoting awareness and reducing the spread of diabetes risk compared to word-of-mouth communication alone. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025.
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.

2025

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