AMAR NATH CHATTERJEE
@magadhuniversity.ac.in
Assistant Professor
Magadh University
RESEARCH, TEACHING, or OTHER INTERESTS
Modeling and Simulation, Ecology, Evolution, Behavior and Systematics, Applied Mathematics
Scopus Publications
Scopus Publications
Jayanta Mondal, Piu Samui, Amar Nath Chatterjee, and Bashir Ahmad
Elsevier BV
Amar Nath Chatterjee, Santosh Kumar Sharma, and Fahad Al Basir
MDPI AG
Measles is the most infectious disease with a high basic reproduction number (R0). For measles, it is reported that R0 lies between 12 and 18 in an endemic situation. In this paper, a fractional order mathematical model for measles disease is proposed to identify the dynamics of disease transmission following a declining memory process. In the proposed model, a fractional order differential operator is used to justify the effect and success rate of vaccination. The total population of the model is subdivided into five sub-compartments: susceptible (S), exposed (E), infected (I), vaccinated (V), and recovered (R). Here, we consider the first dose of measles vaccination and convert the model to a controlled system. Finally, we transform the control-induced model to an optimal control model using control theory. Both models are analyzed to find the stability of the system, the basic reproduction number, the optimal control input, and the adjoint equations with the boundary conditions. Also, the numerical simulation of the model is presented along with using the analytical findings. We also verify the effective role of the fractional order parameter alpha on the model dynamics and changes in the dynamical behavior of the model with R0=1.
Sourav Rana, Amar Nath Chatterjee, and Fahad Al Basir
Springer Science and Business Media LLC
Bo Wang, Jayanta Mondal, Piu Samui, Amar Nath Chatterjee, and Abdullahi Yusuf
Springer Science and Business Media LLC
Santosh Kumar Sharma, Amar Nath Chatterjee, and Fahad Al Basir
Elsevier BV
Santosh Kumar Sharma, Amar Nath Chatterjee, and Bashir Ahmad
MDPI AG
The effect of antiviral therapy during Hepatitis C Virus (HCV) infection is the focus of this study. HCV infection destroys healthy hepatocyte cells in the human liver, causing cirrhosis and hepatocellular carcinoma. We introduce a cell-population model representing the long-term dynamics of HCV infection in response to antiviral drug therapies. The proliferation of existing cells can create hepatocyte cells in the system. Such models are based on the dynamics of susceptible hepatocytes, infected hepatocytes and HCV with interactive dynamics, which can give a complete understanding of the host dynamics of the system in the presence of antiviral drug therapy. Infection-free equilibrium and endemic equilibrium are two equilibrium states in the absence of drugs. The existence and stability conditions for both systems are presented. We also construct an optimal control system to find the optimal control strategy. Numerical results show that the effects of the proliferation rate and infection rate are critical for the changes in the dynamics of the model. The impact of different weight factors on the optimal control problem is analysed through numerical simulation.
Piu Samui, Jayanta Mondal, Bashir Ahmad, and Amar Nath Chatterjee
Springer Science and Business Media LLC
Jayanta Mondal, Piu Samui, and Amar Nath Chatterjee
Springer Science and Business Media LLC
Amar Nath Chatterjee, Fahad Al Basir, Dibyendu Biswas, and Teklebirhan Abraha
MDPI AG
Mathematical modeling is crucial to investigating tthe ongoing coronavirus disease 2019 (COVID-19) pandemic. The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower respiratory tract. During this viral infection, infected cells can activate innate and adaptive immune responses to viral infection. Immune response in COVID-19 infection can lead to longer recovery time and more severe secondary complications. We formulate a micro-level mathematical model by incorporating a saturation term for SARS-CoV-2-infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points have been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for R0<1, and endemic equilibrium exists and is globally stable for R0>1. Impulsive application of drug dosing has been applied for the treatment of COVID-19 patients. Additionally, the dynamics of the impulsive system are discussed when a patient takes drug holidays. Numerical simulations support the analytical findings and the dynamical regimes in the systems.
Bo Wang, Jayanta Mondal, Piu Samui, Amar Nath Chatterjee, and Abdullahi Yusuf
Springer Science and Business Media LLC
Jayanta Mondal, Piu Samui, and Amar Nath Chatterjee
Elsevier BV
Amit Kumar Roy, Fahad Al Basir, Priti Kumar Roy, and Amar Nath Chatterjee
Vilnius University Press
This article deals with a immunological model, which includes multiple classes of T cells, namely, the naive T cell, type I, type II and type 17 T helper cells (Th1, Th2, Th17), regulatory T cell (Treg) along with the activated natural killer cells (NK cells) and epidermal keratinocytes. In order to describe the etiology of psoriasis development, we have studied the basic mathematical properties of the model, existence and stability of the interior equilibrium. We have also derived the drug-induced mathematical model using impulse differential equation to determine the effects of combined biologics Etanercept (TNF-α inhibitor) and Fezakinumab (IL-22 monoclonal antibody) therapy considering perfect dosing during the inductive phase. We have determined the required dosing interval of both drugs to maintain the keratinocytes concentration below a threshold level. This study shows that Etanercept alone could theoretically maintain the keratinocytes level, whereas frequent dosing of Fezakinumab alone may not be enough to control the hyper-proliferation of keratinocytes. Furthermore, combination of the drugs with perfect dosing has the noticeable effect on keratinocytes dynamics, which may be suitable therapeutic approaches for treatment of psoriasis.
Amar Nath Chatterjee, Fahad Al Basir, Bashir Ahmad, and Ahmed Alsaedi
MDPI AG
During the past several years, the deadly COVID-19 pandemic has dramatically affected the world; the death toll exceeds 4.8 million across the world according to current statistics. Mathematical modeling is one of the critical tools being used to fight against this deadly infectious disease. It has been observed that the transmission of COVID-19 follows a fading memory process. We have used the fractional order differential operator to identify this kind of disease transmission, considering both fear effects and vaccination in our proposed mathematical model. Our COVID-19 disease model was analyzed by considering the Caputo fractional operator. A brief description of this operator and a mathematical analysis of the proposed model involving this operator are presented. In addition, a numerical simulation of the proposed model is presented along with the resulting analytical findings. We show that fear effects play a pivotal role in reducing infections in the population as well as in encouraging the vaccination campaign. Furthermore, decreasing the fractional-order parameter α value minimizes the number of infected individuals. The analysis presented here reveals that the system switches its stability for the critical value of the basic reproduction number R0=1.
Amar Nath Chatterjee, Fahad Al Basir, Muqrin A. Almuqrin, Jayanta Mondal, and Ilyas Khan
Elsevier BV
Amar Nath Chatterjee and Bashir Ahmad
Elsevier BV
S. Ghosh, A. N. Chatterjee, P. K. Roy, N. Grigorenko, E. Khailov, and E. Grigorieva
Springer Science and Business Media LLC
Amar Nath Chatterjee, , Fahad Al Basir, Yasuhiro Takeuchi, , and
American Institute of Mathematical Sciences (AIMS)
In this article, we have presented a mathematical model to study the dynamics of hepatitis C virus (HCV) disease considering three populations namely the uninfected liver cells, infected liver cells, and HCV with the aim to control the disease. The model possesses two equilibria namely the disease-free steady state and the endemically infected state. There exists a threshold condition (basic reproduction number) that determines the stability of the disease-free equilibrium and the number of the endemic states. We have further introduced impulsive periodic therapy using DAA into the system and studied the efficacy of the DAA therapy for hepatitis C infected patients in terms of a threshold condition. Finally, impulse periodic dosing with varied rate and time interval is adopted for cost effective disease control for finding the proper dose and dosing interval for the control of HCV disease.
Jayanta Mondal, Piu Samui, and Amar Nath Chatterjee
Taru Publications
Abstract In recent, non-pharmaceutical intervention (lockdown, quarantine, expended testing) and the pharmaceutical intervention (use of commonly used drugs) are the only available strategies to control the COVID-19 disease. Though the scientist all over the world are engaging themselves to find the way out the vaccine of COVID-19, still it is persisted unanswered how to oust the pandemic epidemic from the world. Generally, social distancing, using the mask, etc. are the only available policy to control the pandemic. In this situation uses of common drugs (Azithromycin, HCQ, Antiprotozoal with Doxycycline, Levocetirizine with Montelukast) are common but effective treatment for the reported and hospitalized patient. These drugs activate the immune system of our body to fight against the disease progression. We have formulated a seven compartmental SEIQR type model to explore the COVID-19 disease progression. We have studied the effect of pharmaceutical and non pharmaceutical intervention as a control input and it effect to reduce the number of the infected population while reducing the cost related with the awareness and drug in a specific time frame. Analytical finding tells that the system behavior depends on basic reproduction number and awareness related to social distancing, using the mask and common drug usage are proposed to be sustained so that disease can be controlled. Numerical study support our analytical findings.
Amar Nath Chatterjee and Fahad Al Basir
Hindawi Limited
The current emergence of coronavirus (SARS-CoV-2) puts the world in threat. The structural research on the receptor recognition by SARS-CoV-2 has identified the key interactions between SARS-CoV-2 spike protein and its host (epithelial cell) receptor, also known as angiotensin-converting enzyme 2 (ACE2). It controls both the cross-species and human-to-human transmissions of SARS-CoV-2. In view of this, we propose and analyze a mathematical model for investigating the effect of CTL responses over the viral mutation to control the viral infection when a postinfection immunostimulant drug (pidotimod) is administered at regular intervals. Dynamics of the system with and without impulses have been analyzed using the basic reproduction number. This study shows that the proper dosing interval and drug dose both are important to eradicate the viral infection.
A. Chatterjee and P. Roy
SCIK Publishing Corporation
Smoking habit is an addiction to both physical and psychological. Nicotine from cigarettes temporarily experiences physical withdrawal symptoms and cravings. Because of nicotine effects on the brain, as a quick and reliable way to boost our outlook, relieve stress, and unwind. To stop the smoking habit, you’ll need to address both the addiction and habits. With the proper support and right planning, any smoker can kick the addiction. In this research work, we formulate a mathematical model which analyse the smoking habit in the human population. Here we divide the total population into three classes: potential smokers, smokers and media aware population. We discuss the dynamical behaviour of the model. Finally, we justify our finding through numerical simulation. Our mathematical study reflects that anti smoking campaign plays a pivotal role for reducing number of smoker as well as smoking habit.
Priti Kumar Roy, Amar Nath Chatterjee, and Xue-Zhi Li
World Scientific Pub Co Pte Lt
In this research paper, our main objective is to find out the meticulous role of activated dendritic cells (DCs) during the human immunodeficiency virus (HIV) infection process. DCs play a dual role by enhancing both HIV infection progression, as well as antiviral immune response. To explore the implications of these dual roles, we have formulated our mathematical model and analyzed the model by both analytical and numerical approaches. By using an impulsive differential equation, we have studied the effect of DC-based vaccination. Analytically we have determined the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that, systematic drug dose of the immune cells leads to its maximum level.
PRITI KUMAR ROY, SONIA CHOWDHURY, AMAR NATH CHATTERJEE, JOYDEV CHATTOPADHYAY, and RACHEL NORMAN
World Scientific Pub Co Pte Ltd
Bonhoeffer et al.1studied the long-term dynamics of HIV drug therapy and virus load dynamics. It is well known that highly active anti retroviral therapy (HAART) can effectively control the HIV replication. It is also well known that reverse transcriptase inhibitors (RTIs) could block new infection and as a result control HIV infection. The positive feedback control on such dynamics plays an important role and CD4+T cells are not only produced from a source but also produced from existing T cells. The present investigation takes into account these factors in the original model of Bonhoeffer et al. The optimal control therapy and the effect of time delay in the positive feedback control function have been investigated. Numerical simulation of the nonlinear model has confirmed our analytical studies.
Priti Kumar Roy, Amar Nath Chatterjee, David Greenhalgh, and Qamar J.A. Khan
Elsevier BV
Amar Nath Chatterjee and Priti Kumar Roy
Informa UK Limited
Recent development in antiretroviral treatment against HIV can help AIDS patients to fight against HIV. But the question that whether the disease is to be partially or totally eradicated from HIV infected individuals still remains unsolved. Usually, the most effective treatment for the disease is HAART which can only control the disease progression. But as the immune system becomes weak, the patients can not fight against other diseases. Immune cells are activated and proliferated by IL-2 after the identification of antigen. IL-2 production is impaired in HIV positive patients and intermitted administration of immune activator IL-2 together with HAART which is a more effective treatment to fight against the disease. Thus, its expediency is essential and is yet to be explored. In this article we anticipated a mathematical model of the effect of IL-2 together with RTIs therapy in HIV positive patients. Our analytical as well as numerical study shows that the optimal schedule of treatment for best result is to be obtained by systematic drug therapy. But at the last stage of treatment, the infection level raises again due to minimisation of drug dosage. Thus we study the perfect adherence of the drugs and found out if RTIs are taken with sufficient interval then for fixed interval of IL-2 therapy, certain amount of drug dosages may be able to sustain the immune system at pre-infection stage and the infected CD4+T cells are going towards extinction.