Modeling the intracellular pathogen-immune interaction with cure rate

Dubey, B.; Dubey, Preeti; Dubey, Uma S.

doi:10.1016/j.cnsns.2016.02.007

Cited by 19 publications

(11 citation statements)

References 20 publications

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“…Uninfected cells grow from the sources inside the body (thymus) at rate constant λ and die out at rate δ 0 x. As shown in our previous work [4], the infection rate f (t) = αx(t)v(t) increases linearly with x or with v, which may not be realistic in real life. If we take the saturated incidence rate…”

Section: The Mathematical Modelmentioning

confidence: 92%

“…In the literature, numerous mathematical models have been developed to study the dynamics of HIV infection [1,4,9,17,18,[24][25][26]29,41,42]. The basic viral dynamics model has been studied in detail by researchers [1,24]:…”

Section: Mathematical Models For Hiv Infectionmentioning

confidence: 99%

“…In most of the previous work, it has been observed that immune response increases either due to infected cells (CTL immune response) [24,37,38] or virus (humoral immunity [18]). In this study, we assume that the immune response increases due to infected cells as well as virus (as considered in our previous study [4,7,8]). Keeping the above aspects in view, the virus dynamics can be governed by system (2) of five ordinary differential equations.…”

Section: The Mathematical Modelmentioning

confidence: 99%

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Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response

Dubey

2021

NAMC

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Virus dynamics models are useful in interpreting and predicting the change in viral load over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B virus (HBV).We propose a mathematical model involving the role of total immune response (innate, CTL, and humoral) and treatment for productively infected cells and free virus to understand the dynamics of virus–host interactions. A threshold condition for the extinction or persistence of infection, i.e. basic reproductive number, in the presence of immune response (RI ) is established. We study the global stability of virus-free equilibrium and interior equilibrium using LaSalle’s principle and Lyapunov’s direct method. The global stability of virus-free equilibrium ensures the clearance of virus from the body, which is independent of initial status of subpopulations. Central manifold theory is used to study the behavior of equilibrium points at RI = 1, i.e. when the basic reproductive number in the presence of immune response is one. A special case, when the immune response (IR) is not present, has also been discussed. Analysis of special case suggests that the basic reproductive number in the absence of immune response R0 is greater than that of in the presence of immune response RI , i.e. R0> RI . It indicates that infection may be eradicated if RI < 1. Numerical simulations are performed to illustrate the analytical results using MatLab and Mathematica.

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Section: The Mathematical Modelmentioning

confidence: 92%

Section: Mathematical Models For Hiv Infectionmentioning

confidence: 99%

Section: The Mathematical Modelmentioning

confidence: 99%

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Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response

Dubey

2021

NAMC

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“…Pada beberapa kasus infeksi virus, jumlah pengurangan virion dalam darah lebih banyak dibandingkan jumlah partikel virus yang terlibat dalam proses adsorpsi pada sel rentan. Oleh karena itu, adsorpsi penting untuk diperhatikan, dikarenakan dapat mempengaruhi secara langsung perilaku dinamik model, seperti yang telah dijelaskan oleh Dubey et al [8] dan Pradeep et al [9].…”

Section: Pendahuluanunclassified

Model Matematika Infeksi Virus Hepatitis B dengan Adsorpsi

Sari

2017

JMI

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AbstrakInfeksi Hepatitis B terus berlanjut menjadi masalah kesehatan global. Termotivasi hal tersebut, kami memperkenalkan model matematika infeksi virus Hepatitis B (VHB). Berangkat dari fakta bahwa tingkat infeksi bilinear tidak selalu benar dalam menggambarkan interaksi virus dengan sel rentan di kehidupan nyata, maka digunakan tingkat infeksi nonlinear pada model. Fase adsorpsi dalam proses infeksi virus dipertimbangkan dalam model sebagai salah satu penyebab penurunan populasi partikel virus. Pada model, populasi partikel virus dibagi menjadi dua kompartemen yaitu, virion dan kapsid intraseluler yang mengandung DNA-VHB. Populasi sel dibagi menjadi dua kompartemen yaitu, sel rentan dan sel terinfeksi. Perilaku dinamik model dianalisis dengan menentukan titik kesetimbangan bebas infeksi dan endemik, bilangan reproduksi dasar, serta kestabilan lokal dari titik kesetimbangan tersebut. Hasil analisis dan simulasi numerik menunjukkan bahwa stabilitas titik kesetimbangan bebas infeksi maupun endemik bergantung pada bilangan reproduksi dasar. Kata kunci: adsorpsi, analisis dinamik, bilangan reproduksi dasar, model matematika, virus Hepatitis B. AbstractHepatitis B infection continues to be a global health problem. Motivated with this, we introduce a mathematical model of hepatitis B virus infection (HBV). Based on the fact that bilinear infection rate is not always true in describing viral interactions with susceptible cells in real life, we use nonlinear infection rate on the model. The adsorption phase in the viral infection process is considered in the model as one of the causes of the population decline in viral particles. In the model, the viral particle population is divided into two compartments:, virions and intracellular capsid containing HBV-DNA. Cell population is divided into two compartments: susceptible cells and infected cells. The dynamic behavior of the model is analyzed by determining the free-infection equilibrium point and endemic equilibrium point, the basic reproduction number, and the local stability of the equilibrium points. The analysis and numerical simulation results show that the stability of the equilibriia, free-infection or endemic, depend on the basic reproduction number.

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“…Recently, B. Dubey et. al., [23] investigated the intracellular pathogen-immune interaction with cure rate. They observed that the effect of cure in infected cells through non-cytolytic process has also been observed and found a decrease in infected cells and subsequent increase in uninfected cells.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Pathogen-Immune Interaction Dynamics with Three Time delays

Krishnapriya

2017

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Modeling the intracellular pathogen-immune interaction with cure rate

Cited by 19 publications

References 20 publications

Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response

Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response

Model Matematika Infeksi Virus Hepatitis B dengan Adsorpsi

Analysis of Pathogen-Immune Interaction Dynamics with Three Time delays

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