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  1. Article ; Online: Roles of astrocytes and prions in Alzheimer's disease: insights from mathematical modeling.

    Maji, Mitali / Khajanchi, Subhas

    Journal of biological physics

    2023  

    Abstract: We present a mathematical model that explores the progression of Alzheimer's disease, with a particular focus on the involvement of disease-related proteins and astrocytes. Our model consists of a coupled system of differential equations that delineates ... ...

    Abstract We present a mathematical model that explores the progression of Alzheimer's disease, with a particular focus on the involvement of disease-related proteins and astrocytes. Our model consists of a coupled system of differential equations that delineates the dynamics of amyloid beta plaques, amyloid beta protein, tau protein, and astrocytes. Amyloid beta plaques can be considered fibrils that depend on both the plaque size and time. We change our mathematical model to a temporal system by applying an integration operation with respect to the plaque size. Theoretical analysis including existence, uniqueness, positivity, and boundedness is performed in our model. We extend our mathematical model by adding two populations, namely prion protein and amyloid beta-prion complex. We characterize the system dynamics by locating biologically feasible steady states and their local stability analysis for both models. The characterization of the proposed model can help inform in advancing our understanding of the development of Alzheimer's disease as well as its complicated dynamics. We investigate the global stability analysis around the interior equilibrium point by constructing a suitable Lyapunov function. We validate our theoretical analysis with the aid of extensive numerical illustrations.
    Language English
    Publishing date 2023-12-29
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2016734-9
    ISSN 1573-0689 ; 0092-0606
    ISSN (online) 1573-0689
    ISSN 0092-0606
    DOI 10.1007/s10867-023-09652-0
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  2. Article: Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak.

    Mondal, Jayanta / Khajanchi, Subhas

    Nonlinear dynamics

    2022  Volume 109, Issue 1, Page(s) 177–202

    Abstract: 34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social ... ...

    Abstract 34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (
    Supplementary information: The online version supplementary material available at 10.1007/s11071-022-07235-7.
    Language English
    Publishing date 2022-01-30
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2012600-1
    ISSN 1573-269X ; 0924-090X
    ISSN (online) 1573-269X
    ISSN 0924-090X
    DOI 10.1007/s11071-022-07235-7
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  3. Article ; Online: An eco-epidemiological model with the impact of fear.

    Sarkar, Kankan / Khajanchi, Subhas

    Chaos (Woodbury, N.Y.)

    2022  Volume 32, Issue 8, Page(s) 83126

    Abstract: In this study, we propose and analyze an eco-epidemiological model with disease in prey and incorporated the effect of fear on prey species due to predator population. We assume that the prey population grows logistically in the absence of predator ... ...

    Abstract In this study, we propose and analyze an eco-epidemiological model with disease in prey and incorporated the effect of fear on prey species due to predator population. We assume that the prey population grows logistically in the absence of predator species, and the disease is limited to the prey population only. We divide the total prey population into two distinct classes: susceptible prey and infected prey. Predator populations are not infected by the diseases, though feed both the susceptible and infected prey. Due to the fear of predators, the prey population becomes more vigilant and moves away from suspected predators. Such a foraging activity of prey reduces the chance of infection among susceptible prey by lowering the contact with infected prey. We assume that the fear of predators has no effect on infected prey as they are more vigilant. Positivity, boundedness, and uniform persistence of the proposed model are investigated. The biologically feasible equilibrium points and their stability are analyzed. We establish the conditions for the Hopf bifurcation of the proposed model around the endemic steady state. As the level of fear increases, the system moves toward the steady state from a limit cycle oscillation. The increasing level of fear cannot wipe out the diseases from the system, but the amplitude of the infected prey decreases as the level of fear is increased. The system changes its stability as the rate of infection increases, and the predator becomes extinct when the rate of infection in prey is high enough though predators are not infected by the disease.
    MeSH term(s) Animals ; Ecosystem ; Epidemiological Models ; Fear ; Models, Biological ; Population Dynamics ; Predatory Behavior
    Language English
    Publishing date 2022-08-17
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0099584
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  4. Article ; Online: Spatiotemporal dynamics of a glioma immune interaction model.

    Khajanchi, Subhas / Nieto, Juan J

    Scientific reports

    2021  Volume 11, Issue 1, Page(s) 22385

    Abstract: We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion ... ...

    Abstract We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.
    MeSH term(s) Algorithms ; Biomarkers, Tumor ; Disease Susceptibility/immunology ; Glioma/etiology ; Humans ; Models, Biological ; Spatio-Temporal Analysis
    Chemical Substances Biomarkers, Tumor
    Language English
    Publishing date 2021-11-17
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/s41598-021-00985-1
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  5. Article ; Online: Modeling the dynamics of COVID-19 pandemic with implementation of intervention strategies.

    Khajanchi, Subhas / Sarkar, Kankan / Banerjee, Sandip

    European physical journal plus

    2022  Volume 137, Issue 1, Page(s) 129

    Abstract: The ongoing COVID-19 epidemic spread rapidly throughout India, with 34,587,822 confirmed cases and 468,980 deaths as of November 30, 2021. Major behavioral, clinical, and state interventions have implemented to mitigate the outbreak and prevent the ... ...

    Abstract The ongoing COVID-19 epidemic spread rapidly throughout India, with 34,587,822 confirmed cases and 468,980 deaths as of November 30, 2021. Major behavioral, clinical, and state interventions have implemented to mitigate the outbreak and prevent the persistence of the COVID-19 in human-to-human transmission in India and worldwide. Hence, the mathematical study of the disease transmission becomes essential to illuminate the real nature of the transmission behavior and control of the diseases. We proposed a compartmental model that stratify into nine stages of infection. The incidence data of the SRAS-CoV-2 outbreak in India was analyzed for the best fit to the epidemic curve and we estimated the parameters from the best fitted curve. Based on the estimated model parameters, we performed a short-term prediction of our model. We performed sensitivity analysis with respect to
    Language English
    Publishing date 2022-01-17
    Publishing country Germany
    Document type Journal Article
    ISSN 2190-5444
    ISSN (online) 2190-5444
    DOI 10.1140/epjp/s13360-022-02347-w
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  6. Article: How do the contaminated environment influence the transmission dynamics of COVID-19 pandemic?

    Sarkar, Kankan / Mondal, Jayanta / Khajanchi, Subhas

    The European physical journal. Special topics

    2022  , Page(s) 1–20

    Abstract: COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that first appeared in Wuhan city and then globally. The COVID-19 pandemic exudes public health and socio-economic burden globally. Mathematical modeling plays a significant role to ... ...

    Abstract COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that first appeared in Wuhan city and then globally. The COVID-19 pandemic exudes public health and socio-economic burden globally. Mathematical modeling plays a significant role to comprehend the transmission dynamics and controlling factors of rapid spread of the disease. Researchers focus on the human-to-human transmission of the virus but the SARS-CoV-2 virus also contaminates the environment. In this study we proposed a nonlinear mathematical model for the COVID-19 pandemic to analyze the transmission dynamics of the disease in India. We have also incorporated the environment contamination by the infected individuals as the population density is very high in India. The model is fitted and parameterized using daily new infection data from India. Analytical study of the proposed COVID-19 model, including feasibility of critical points and their stability reveals that the infection-free steady state is stable if the basic reproduction number is less than unity otherwise the system shows significant outbreak. Numerical illustrations demonstrates that if the rate of environment contamination increased then the number of infected persons also increased. But if the environment is disinfected by sanitization then the number of infected persons cannot drastically increase.
    Language English
    Publishing date 2022-08-22
    Publishing country France
    Document type Journal Article
    ZDB-ID 2267176-6
    ISSN 1951-6401 ; 1951-6355
    ISSN (online) 1951-6401
    ISSN 1951-6355
    DOI 10.1140/epjs/s11734-022-00648-w
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  7. Article ; Online: Forecasting the daily and cumulative number of cases for the COVID-19 pandemic in India.

    Khajanchi, Subhas / Sarkar, Kankan

    Chaos (Woodbury, N.Y.)

    2020  Volume 30, Issue 7, Page(s) 71101

    Abstract: The ongoing novel coronavirus epidemic was announced a pandemic by the World Health Organization on March 11, 2020, and the Government of India declared a nationwide lockdown on March 25, 2020 to prevent community transmission of the coronavirus disease ( ...

    Abstract The ongoing novel coronavirus epidemic was announced a pandemic by the World Health Organization on March 11, 2020, and the Government of India declared a nationwide lockdown on March 25, 2020 to prevent community transmission of the coronavirus disease (COVID)-19. Due to the absence of specific antivirals or vaccine, mathematical modeling plays an important role in better understanding the disease dynamics and in designing strategies to control the rapidly spreading infectious disease. In our study, we developed a new compartmental model that explains the transmission dynamics of COVID-19. We calibrated our proposed model with daily COVID-19 data for four Indian states, namely, Jharkhand, Gujarat, Andhra Pradesh, and Chandigarh. We study the qualitative properties of the model, including feasible equilibria and their stability with respect to the basic reproduction number R
    MeSH term(s) Algorithms ; Basic Reproduction Number ; Betacoronavirus ; COVID-19 ; Calibration ; Computer Simulation ; Coronavirus Infections/epidemiology ; Coronavirus Infections/transmission ; Disease Outbreaks ; Forecasting ; Humans ; India/epidemiology ; Linear Models ; Pandemics ; Pneumonia, Viral/epidemiology ; Pneumonia, Viral/transmission ; SARS-CoV-2
    Keywords covid19
    Language English
    Publishing date 2020-07-22
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0016240
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  8. Article ; Online: Forecasting the daily and cumulative number of cases for the COVID-19 pandemic in India

    Khajanchi, Subhas / Sarkar, Kankan

    Chaos: An Interdisciplinary Journal of Nonlinear Science

    2020  Volume 30, Issue 7, Page(s) 71101

    Keywords Mathematical Physics ; General Physics and Astronomy ; Applied Mathematics ; Statistical and Nonlinear Physics ; covid19
    Language English
    Publisher AIP Publishing
    Publishing country us
    Document type Article ; Online
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0016240
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  9. Article: Modeling and forecasting the COVID-19 pandemic in India.

    Sarkar, Kankan / Khajanchi, Subhas / Nieto, Juan J

    Chaos, solitons, and fractals

    2020  Volume 139, Page(s) 110049

    Abstract: In India, 100,340 confirmed cases and 3155 confirmed deaths due to COVID-19 were reported as of May 18, 2020. Due to absence of specific vaccine or therapy, non-pharmacological interventions including social distancing, contact tracing are essential to ... ...

    Abstract In India, 100,340 confirmed cases and 3155 confirmed deaths due to COVID-19 were reported as of May 18, 2020. Due to absence of specific vaccine or therapy, non-pharmacological interventions including social distancing, contact tracing are essential to end the worldwide COVID-19. We propose a mathematical model that predicts the dynamics of COVID-19 in 17 provinces of India and the overall India. A complete scenario is given to demonstrate the estimated pandemic life cycle along with the real data or history to date, which in turn divulges the predicted inflection point and ending phase of SARS-CoV-2. The proposed model monitors the dynamics of six compartments, namely susceptible (S), asymptomatic (A), recovered (R), infected (I), isolated infected (
    Keywords covid19
    Language English
    Publishing date 2020-06-28
    Publishing country England
    Document type Journal Article
    ZDB-ID 2003919-0
    ISSN 1873-2887 ; 0960-0779
    ISSN (online) 1873-2887
    ISSN 0960-0779
    DOI 10.1016/j.chaos.2020.110049
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  10. Article: A mathematical model for COVID-19 transmission dynamics with a case study of India.

    Samui, Piu / Mondal, Jayanta / Khajanchi, Subhas

    Chaos, solitons, and fractals

    2020  Volume 140, Page(s) 110173

    Abstract: The ongoing COVID-19 has precipitated a major global crisis, with 968,117 total confirmed cases, 612,782 total recovered cases and 24,915 deaths in India as of July 15, 2020. In absence of any effective therapeutics or drugs and with an unknown ... ...

    Abstract The ongoing COVID-19 has precipitated a major global crisis, with 968,117 total confirmed cases, 612,782 total recovered cases and 24,915 deaths in India as of July 15, 2020. In absence of any effective therapeutics or drugs and with an unknown epidemiological life cycle, predictive mathematical models can aid in understanding of both coronavirus disease control and management. In this study, we propose a compartmental mathematical model to predict and control the transmission dynamics of COVID-19 pandemic in India with epidemic data up to April 30, 2020. We compute the basic reproduction number
    Keywords covid19
    Language English
    Publishing date 2020-08-05
    Publishing country England
    Document type Journal Article
    ZDB-ID 2003919-0
    ISSN 1873-2887 ; 0960-0779
    ISSN (online) 1873-2887
    ISSN 0960-0779
    DOI 10.1016/j.chaos.2020.110173
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