Shyam Sundar
@psit.ac.in
Professor, Department of Mathematics
Pranveer Singh Institute of Technology, Kanpur
RESEARCH INTERESTS
Mathematical Modeling of Environmental & Ecological Systems
Mathematical Modeling of Epidemiology, Transmission dynamics of HIV/AIDS
Mathematical Modeling of Social Dynamics
Scopus Publications
Scopus Publications
Priya Verma, Maninder Singh Arora, and Shyam Sundar
Springer Science and Business Media LLC
Monika Trivedi, Ram Naresh Tripathi, and Shyam Sundar
Springer Nature Switzerland
Shyam Sundar, A. K. Misra, Ram Naresh, and J. B. Shukla
Springer Science and Business Media LLC
Ram Naresh, Shyam Sundar, Sandhya Rani Verma, and Jang Bahadur Shukla
Walter de Gruyter GmbH
Abstract In this article, a nonlinear mathematical model is proposed and analyzed to study the spread of coronavirus disease (COVID-19) and its control. Due to sudden emergence of a peculiar kind of infection, no vaccines were available, and therefore, the nonpharmaceutical interventions such as lockdown, isolation, and hospitalization were imposed to stop spreading of the infectious disease. The proposed model consists of six dependent variables, namely, susceptible population, infective population, isolated susceptible population who are aware of the undesirable consequences of the COVID-19, quarantined population of known infectives (symptomatic), recovered class, and the coronavirus population. The model exhibits two equilibria namely, the COVID-19-free equilibrium and the COVID-19-endemic equilibrium. It is observed that if basic reproduction number R 0 < 1 {R}_{0}\\lt 1 , then the COVID-19-free equilibrium is locally asymptotically stable. However, the endemic equilibrium is locally as well as nonlinearly asymptotically stable under certain conditions if R 0 > 1 {R}_{0}\\gt 1 . Model analysis shows that if safety measures are adopted by way of isolation of susceptibles and quarantine of infectives, the spread of COVID-19 disease can be kept under control.
S. Sundar, , A. K. Mishra, J. B. Shukla, , and
International Society for Environmental Information Science (ISEIS)
In this paper, a non-linear mathematical model is proposed and analyzed to study the effects of mitigation options on the control of methane emissions in the atmosphere caused by rice paddies and livestock populations to reduce global warming. In the modeling process, it is assumed that the cumulative biomass density of rice paddies and the density of livestock populations follow logistic models with their respective growth rates and carrying capacities. The growth rate of concentration of methane in the atmos- phere is assumed to be directly proportional to the cumulative density of various processes involved in the production of rice paddies as well as the cumulative density of various processes used in the farming of livestock populations. This growth rate is also assumed to increase with natural factors such as wetlands but it decreases with the cumulative density of mitigation options, considered to be pro- portional to the increased level of methane concentration in the atmosphere. The non-linear model is analyzed by using the stability theory of differential equations and computer simulation. The analysis shows that mitigation options can control the methane emissions in the atmosphere caused by rice paddies and livestock populations considerably. The computer simulation of the model confirms this analytical result. The data from model prediction is compared with actual methane data in the atmosphere and found to be very satisfactory.
J. B. Shukla, Niranjan Swaroop, Shyam Sundar, and Ram Naresh
Springer Science and Business Media LLC
Shyam Sundar, Ashish Kumar Mishra, Ram Naresh, and J. B. Shukla
Springer Science and Business Media LLC
Shyam Sundar, Ashish Kumar Mishra, and Ram Naresh
Springer Science and Business Media LLC
Shyam Sundar and Ram Naresh
Springer Science and Business Media LLC
J.B. Shukla, Mahesh Singh Chauhan, Shyam Sundar, and Ram Naresh
Inderscience Publishers
We propose non–linear models to study the feasibility of removing CO2 from the atmosphere by introducing some external species such as liquid droplets and particulate matters in the atmosphere, which may react with this gas and get it removed by gravity. Further, this gas can also be removed by photosynthesis process upon using plantation of leafy trees around the sources of emission. The proposed nonlinear models are analysed using stability theory of differential equations and computer simulations. Model analysis suggests that the concentration of global warming gas decreases as the rates of introduction of liquid droplets and particulate matters increase. Also, this gas can be removed almost completely from the atmosphere, if the rates of introduction of these external species are very large. The concentration of CO2 also decreases as its absorption by green belt increases. It decreases further if the rate of introduction of external species increases. The numerical simulation of the models confirms these analytical results.
J. B. Shukla, Shyam Sundar, A. K. Misra, and Ram Naresh
Springer Science and Business Media LLC
J. B. SHUKLA, SHYAM SUNDAR, SHIVANGI -, and RAM NARESH
Wiley
Abstract In this paper, a nonlinear mathematical model is proposed and analyzed to study the formation of acid rain in the atmosphere because of precipitation and its effect on plant species. It is considered that acid‐forming gases such as SO2, NO2 emitted from various sources combine with water droplets (moisture) during precipitation and form acid rain affecting plant species. It is assumed that the biomass density of plant species follows a logistic model and its growth rate decreases with increase in the concentration of acid rain. The model is analyzed by using stability theory of differential equations and numerical simulation. The model analysis shows that as the concentration of acid rain increases because of increase in the cumulative emission rates of acid forming gases, the biomass density of plant species decreases. It is noted that if the amount of acid formed becomes very large, the plant species may become extinct.
Shyam Sundar, Ram Naresh, A.K. Misra, and J.B. Shukla
Elsevier BV
J.B. Shukla, A.K. Misra, Shyam Sundar, and Ram Naresh
Elsevier BV
J. B. Shukla, Shyam Sundar, A. K. Misra, and Ram Naresh
Springer Science and Business Media LLC
Ram Naresh, Shyam Sundar, and J.B. Shukla
Elsevier BV
Ram Naresh, Shyam Sundar, and J.B. Shukla
Elsevier BV
Ram Naresh, Shyam Sundar, and J.B. Shukla
Elsevier BV
R. Naresh, S. Sundar, and R. K. Upadhyay
Walter de Gruyter GmbH
A nonlinear mathematical model is proposed and analyzed to study the removal of primary and secondary air pollutants by precipitation in the atmosphere. The atmosphere, under consideration, consists of four interacting phases i.e. the rain droplets phase, the primary pollutants phase, the secondary pollutants phase and the combined phase of these pollutants absorbed in the rain droplets. The dynamics of these phases is governed by the ordinary differential equations with source, nonlinear interaction, conversion and removal terms. The proposed model is analyzed qualitatively using stability theory of differential equations. It is shown that under appropriate conditions, the pollutants can be removed from the atmosphere significantly and the removed amount would depend upon the rate of introduction of primary pollutants, rate of formation of secondary pollutants, rate of precipitation, rate of absorption and rate of falling rain droplets on the ground. Finally, computer simulations are performed to investigate the dynamics of model system. The results obtained in the paper are found to be in line with the experimental observations published in the literature.