Chandra Nath Podder

University of Dhaka · Department of Mathematics

Rumors are relentlessly pervasive in social and organizational settings, enduring through time. They grab attention, ignite emotions, compel participation, shape attitudes and behaviors, and are omnipresent. As electronic technology advances and network platforms become more diverse, there is growing interest in conducting comprehensive research on...

In this paper, the Caputo fractional derivative is assumed to be the prey–predator model. In order to create Caputo fractional differential equations for the prey–predator model, a discretization process is first used. The fixed points of the model are categorized topologically. We identify requirements for the fixed points of the suggested prey–pr...

A mathematical model considering two strains of hepatitis B virus (HBV) chronic carriers, to assess the impact of dose-structured imperfect vaccine, in a population, is designed and analyzed. The model is shown to have a locally and globally asymptotically stable disease-free equilibrium (DFE) whenever its associated reproduction number is numerica...

A model for assessing the impact of key population at risk in spreading HIV/AIDS is designed. The model is shown to have a globally asymptotically stable (GAS) disease-free equilibrium whenever the associated reproduction number is less than unity. It has a unique GAS endemic equilibrium whenever reproduction number exceeds unity, if there is no ba...

In this paper, a deterministic compartmental model is presented to assess the impact of vaccination and non-pharmaceutical interventions (social distance, awareness, face mask, and quarantine) on the transmission dynamics of COVID-19 with co-morbidity and re-infection. An expression for the basic reproduction number is then derived for this model....

A novel coronavirus (COVID-19) has emerged as a global serious public health issue from December 2019. People having a weak immune system are more susceptible to coronavirus infection. It is a double challenge for people of any age with certain underlying medical conditions including cardiovascular disease, diabetes, high blood pressure and cancer...

In this paper, a deterministic model for the dynamics of chikungunya virus transmission is formulated and analyzed. It is shown that the model has a disease free equilibrium (DFE) and by using the basic reprodution number (R0) local stability of DFE is proved when R0 < 1. Also, the global stability of DFE is investigated by Lyapunov function and La...

In this paper, we study a new IVESR rumor spreading model with hesitating and forgetting mechanisms in homogeneous network. The rumor free and rumor prevailing equilibriums, and the basic reproduction number ℜ 0 are calculated from the mean-field equations of the model. The local and global stability of rumor free equilibrium are proved by using Ly...

A new mathematical model of chronic hepatitis C virus (HCV) infection incorporating humoral and cell-mediated immune responses, distinct cell proliferation rates for both uninfected and infected hepatocytes, and antiviral treatment all at once, is formulated and analysed meticulously. Analysis of the model elucidates the existence of multiple equil...

A new mathematical model of chronic hepatitis C virus (HCV) infection incorporating humoral and cell-mediated immune responses, distinct cell proliferation rates for both uninfected and infected hepatocytes, and antiviral treatment all at once, is formulated and analysed meticulously. Analysis of the model elucidates the existence of multiple equil...

The distribution of HIV and malaria overlap globally. So there is always a chance of co-infection. In this paper the impact of medication on HIV-Malaria co-infection has been analyzed and we have developed a mathematical model using the idea of the models of Mukandavire, et al. [13] and Barley, et al. [3] where treatment classes are included. The d...

In this paper, the discrete time generalized Hénon map is considered and the existence of Hopf bifurcation via an explicit criterion for N≥3, in particular for N=4 and N=5 has given. The relation between the parameters a and b as well as the range of the values of the parameters for N=3,4,5 has driven and the existence of Hopf bifurcation is demons...

As mosquito vector plays a significant role in malaria dynamics, a deterministic delay differential equation model 10 for the population dynamics of the malaria vector is rigorously analyzed for the non-delay part subject to a new form of vector birth rate function; the Hassell function. For the Hassell function, the model has a non-trivial equil...

A new deterministic model for Herpes Simplex Virus-2 (HSV-2) in vivo, which incorporates the cell-mediated and humoral immune responses, is designed and analyzed. The analyses of the model reveal that it has a globally-asymptotically stable (GAS) virus-free equilibrium (VFE) whenever the associated reproduction threshold is less than unity. Also, i...

The optimal use of intervention strategies to mitigate the spread of Nipah Virus (NiV) using optimal control technique is studied in this paper. First of all we formulate a dynamic model of NiV infections with variable size population and two control strategies where creating awareness and treatment are considered as controls. We intend to find the...

In this Paper we formulate a mathematical model of dengue virus transmission in the human body to monitor the effects of migratory population and some control strategies at aquatic and adult stages of vector(mosquito). The model has a locally asymptotically stable disease-freeequilibrium (DFE) whenever a certain epidemiological threshold, known as...

Mathematical models and underlying transmission mechanism of the HIV and HSV-2 can help the scientific, medical and researcher to understand and anticipate their spread in different population. Present study fitted mathematical models, which exhibit two equilibriums namely, the disease free and the endemic equilibrium. It is found that if the basic...

In this paper, we have rigorously analyzed a model to find the effective control strategies on the transmission dynamics of a vector-borne disease. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. The numerical simulations (using MatLab and Maple) of the model reveal that the precautio...

A risk-structured, two-sex, model for the transmission dynamics of herpes simplex virus type 2 (HSV-2) in a population is designed and qualitatively analyzed. It is shown that adding risk structure (i.e., the risk of transmitting or acquiring HSV-2 infection) to an HSV-2 transmission model causes the phenomenon of backward bifurcation when the asso...

This paper characterizes the qualitative dynamics of a vaccination model, with waning natural and vaccine-induced immunity, representing the transmission of an infectious agent in a population. The deterministic SIRS model with vaccination undergoes backward bifurcation when the associated reproduction number (Rv) is less than unity. It is shown th...

This paper presents a deterministic model for evaluating the impact of anti-retroviral drugs (ARVs), voluntary testing (using standard antibody-based and a DNA-based testing methods) and condom use on the transmission dynamics of HIV in a community. Rigorous qualitative analysis of the model show that it has a globally-stable disease-free equilibri...

The paper presents a deterministic compartmental model for the transmission dynamics of swine influenza (H1N1) pandemic in a population in the presence of an imperfect vaccine and use of drug therapy for confirmed cases. Rigorous analysis of the model, which stratifies the infected population in terms of their risk of developing severe illness, rev...

A new mathematical model for the transmission dynamics of herpes simplex virus type 2 (HSV-2), which takes into account disease transmission by infected individuals in the quiescent state and an imperfect HSV-2 vaccine, is designed and qualitatively analysed. In the absence of vaccination, it is shown that the model has a globally asymptotically st...

A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite) in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features. It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotical...

A new sex-structured deterministic model for the transmission dynamics of Herpes Simplex Virus type 2 (HSV-2) is designed and qualitatively analysed. The model has a globally-asymptotic stable (GAS) disease-free equilib-rium (DFE) whenever the associated reproduction threshold is less than unity. Further, it has a unique endemic equilibrium (EEP),...

This paper presents a deterministic model for the transmission dynamics of Mycobacterium tuberculosis (TB) in a population in the presence of Directly Observed Therapy Short-course (DOTS). The model, which allows for the detection and treatment of individuals with symptoms and uses standard incidence function for the infection rate, is rigorously a...

This paper addresses the synergistic interaction between HIV and mycobacterium tuberculosis using a deterministic model, which incorporates many of the essential biological and epidemiological features of the two dis- eases. In the absence of TB infection, the model (HIV-only model) is shown to have a globally asymptotically stable, disease-free eq...

The phenomenon of backward bifurcation in disease models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has important implications for disease control. In such a scenario, the classical requirement of the reproduction number being less than unity becom...

A recent randomized controlled trial shows a significant reduction in women-to-men transmission of HIV due to male circumcision. Such development calls for a rigorous mathematical study to ascertain the full impact of male circumcision in reducing HIV burden, especially in resource-poor nations where access to anti-retroviral drugs is limited. Firs...

The quarantine of suspected cases and isolation of individuals with symptoms are two of the primary public health control measures for combating the spread of a communicable emerging or re-emerging disease. Implementing these measures, however, can inflict significant socio-economic and psychological costs. This paper presents a deterministic compa...

We investigate the dynamics of a delay difference equation by considering the dynamics of a planar map. The analysis uses the symbolic and computational capability of Mathematica.

We studied stability analysis of a chemostat model of two microorganisms that incorporates both different response functions and we made a single code of the model using a computer algebra system (CAS) Mathematica for graphical illustration globally.