MODELING EFFECTS OF TOXICANT ON UNINFECTED CELLS, INFECTED CELLS AND IMMUNE RESPONSE IN THE PRESENCE OF VIRUS

2011 ◽  
Vol 19 (03) ◽  
pp. 479-503 ◽  
Author(s):  
B. DUBEY ◽  
UMA S. DUBEY ◽  
J. HUSSAIN
Keyword(s):  
Immune Response ◽  
Mathematical Models ◽  
Global Stability ◽  
Computer Simulations ◽  
Local Stability ◽  
Sufficient Conditions ◽  
The Body ◽  
Environmental Toxicant ◽  
Infected Cells

In this paper, two mathematical models are proposed and analyzed. The first one deals with the interaction of uninfected cells, infected cells, viruses and immune response within humans. The second one deals with the effects of environmental toxicant on the first model. In each case, sufficient conditions for local stability and global stability of the equilibria are obtained, computer simulations are performed and the result is biologically interpreted. It has been seen that the environmental toxicant has detrimental effects on healthy cells, infected cells as well as on the immune response of the body.

A MATHEMATICAL MODEL FOR THE EFFECT OF TOXICANT ON THE IMMUNE SYSTEM

2007 ◽  
Vol 15 (04) ◽  
pp. 473-493 ◽  
Author(s):  
UMA S. DUBEY ◽  
BALRAM DUBEY
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Immune System ◽  
Local Stability ◽  
Defense Mechanism ◽  
Oscillatory Behavior ◽  
The Body ◽  
Nonlinear Mathematical Model ◽  
Environmental Toxicant ◽  
Equilibrium Level

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effect of environmental toxicant on the immune response of the body. Criteria for local stability, instability and global stability are obtained. It is shown that the immune response of the body decreases as the concentration of environmental toxicant increases, and certain criteria are obtained under which it settles down at its equilibrium level. In the absence of toxicant, an oscillatory behavior of immune system and pathogenic growth is observed. However, in the presence of toxicant, oscillatory behavior is not observed. These studies show that the toxicant may have a grave effect on our body's defense mechanism.

scholarly journals Global Stability of Humoral Immunity HIV Infection Models with Chronically Infected Cells and Discrete Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-25
Author(s):  
A. M. Elaiw ◽  
N. A. Alghamdi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Incidence Rate ◽  
Sufficient Conditions ◽  
Humoral Immune ◽  
Infection Models ◽  
Existence And Stability ◽  
Discrete Delays ◽  
Infected Cells ◽  
Theoretical Results

We study the global stability of three HIV infection models with humoral immune response. We consider two types of infected cells: the first type is the short-lived infected cells and the second one is the long-lived chronically infected cells. In the three HIV infection models, we modeled the incidence rate by bilinear, saturation, and general forms. The models take into account two types of discrete-time delays to describe the time between the virus entering into an uninfected CD4+T cell and the emission of new active viruses. The existence and stability of all equilibria are completely established by two bifurcation parameters,R0andR1. The global asymptotic stability of the steady states has been proven using Lyapunov method. In case of the general incidence rate, we have presented a set of sufficient conditions which guarantee the global stability of model. We have presented an example and performed numerical simulations to confirm our theoretical results.

GLOBAL STABILITY OF A CHEMOSTAT MODEL WITH DELAYED RESPONSE IN GROWTH AND A LETHAL EXTERNAL INHIBITOR

2008 ◽  
Vol 01 (04) ◽  
pp. 503-520 ◽  
Author(s):  
ZHIQI LU ◽  
JINGJING WU
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Delayed Response ◽  
Qualitative Properties ◽  
Chemostat Model ◽  
Stability And Instability ◽  
Discrete Delays ◽  
Globally Stable

A competition model between two species with a lethal inhibitor in a chemostat is analyzed. Discrete delays are used to describe the nutrient conversion process. The proved qualitative properties of the solution are positivity, boundedness. By analyzing the local stability of equilibria, it is found that the conditions for stability and instability of the boundary equilibria are similar to those in [9]. In addition, the global asymptotic behavior of the system is discussed and the sufficient conditions for the global stability of the boundary equilibria are obtained. Moreover, by numerical simulation, it is interesting to find that the positive equilibrium may be globally stable.

Correlation between Platelet to Lymphocyte Ratio with C-Reactive Protein in COVID-19 Patients

2021 ◽  
Vol 28 (1) ◽  
pp. 17
Author(s):  
Novianti Anggie Lestari ◽  
Dwi Retnoningrum
Keyword(s):  
Immune Response ◽  
T Cells ◽  
Cytotoxic T Cells ◽  
The Body ◽  
Cross Sectional ◽  
Reactive Protein ◽  
A Value ◽  
Infected Cells ◽  
Spearman Test ◽  
Moderate Positive Correlation

Coronavirus 2019 (COVID-19) is an infectious disease caused by Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). Inflammation occurs when the body is infected with the virus. Platelets play a role in immune response and immunomodulation by activating P-Selectin Glycoprotein (PSGL) to the site of inflammation. Lymphocytes play a role through CD4 T-cells, B-cells producing specific viral antibodies, and CD8 cytotoxic T-cells by directly killing the virus in infected cells. This study aimed to prove the correlation between PLR and CRP as inflammation markers in COVID-19 patients. This study was a retrospective observational study with the cross-sectional approach at Dr. Kariadi Hospital, Semarang, for the period March-August 2020. Spearman test performed for analyzing data with p<0.05 was significant. Thirty-three confirmed COVID-19 patients with median value of PLR 218 (103-1609) and CRP 15.94 (1.24-200) mg/L were tested for correlation with a value of p=0.013 and r=0.427. The increase of PLR and CRP in COVID-19 patients was caused by an inflammatory process mediated by the immune response. High values in the blood were associated with disease severity and poor prognosis. There was a statistically significant moderate positive correlation between PLR and CRP in COVID-19 patients.

Persistence and Extinction of One-Prey and Two-Predators System

2004 ◽  
Vol 9 (4) ◽  
pp. 307-329 ◽  
Author(s):  
B. Dubey ◽  
R. K. Upadhyay
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Global Stability ◽  
Computer Simulations ◽  
Local Stability ◽  
Ratio Dependent

In this paper, a mathematical model is proposed and analysed to study the dynamics of one-prey two-predators system with ratio-dependent predators growth rate. Criteria for local stability, instability and global stability of the nonnegative equilibria are obtained. The permanent co-existence of the three species is also discussed. Finally, computer simulations are performed to investigate the dynamics of the system.

Global stability and Hopf bifurcation of an eco-epidemiological model with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950062
Author(s):  
Jinna Lu ◽  
Xiaoguang Zhang ◽  
Rui Xu
Keyword(s):  
Time Delay ◽  
Global Stability ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Epidemiological Model ◽  
Hopf Bifurcations ◽  
Lyapunov Functionals ◽  
Predator Population ◽  
Disease Free ◽  
Transmissible Disease

In this paper, an eco-epidemiological model with time delay representing the gestation period of the predator is investigated. In the model, it is assumed that the predator population suffers a transmissible disease and the infected predators may recover from the disease and become susceptible again. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free and coexistence equilibria are established, respectively. By means of Lyapunov functionals and LaSalle’s invariance principle, sufficient conditions are obtained for the global stability of the coexistence equilibrium, the disease-free equilibrium and the predator-extinct equilibrium of the system, respectively.

scholarly journals Global dynamics of humoral and cellular immune responses to virus infection

2019 ◽  
Vol 24 (2) ◽  
pp. 407-423 ◽  
Author(s):  
Miller Cerón-Gómez ◽  
Hyun Mo Yang
Keyword(s):  
Immune Response ◽  
Immune Responses ◽  
Global Stability ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Reproductive Number ◽  
Target Cells ◽  
Global Dynamics ◽  
Cellular Immune Responses ◽  
Cellular Immune

We study the global stability of a model of virus dynamics with consideration of humoral and cellular immune responses. We use a Lyapunov direct method to obtain sufficient conditions for the global stability of virus free and viruspresence equilibriums. First, we analyze the model without an immune response and found that if the reproductive number of the virus is less than or equal to one, the virus-free equilibrium is globally asymptotically stable. However, for the virus-presence equilibrium, global stability is obtained if the virus entrance rate into the target cells is less than one. We analyze the model with humoral and cellular immune responses and found similar results. The difference is that in the reproductive number of the virus and in the virus entrance rate into the target cells appear parameters of humoral and cellular immune responses, which means that the adaptive immune response will cease or control the rise of the infection.

scholarly journals Global Stability of an Eco-Epidemiological Model with Time Delay and Saturation Incidence

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Shuxue Mao ◽  
Rui Xu ◽  
Zhe Li ◽  
Yunfei Li
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Epidemiological Model ◽  
Positive Equilibrium ◽  
Numerical Examples ◽  
Disease In Predator ◽  
Comparison Arguments ◽  
Disease Free ◽  
Iteration Technique

We investigate a delayed eco-epidemiological model with disease in predator and saturation incidence. First, by comparison arguments, the permanence of the model is discussed. Then, we study the local stability of each equilibrium of the model by analyzing the corresponding characteristic equations and find that Hopf bifurcation occurs when the delayτpasses through a sequence of critical values. Next, by means of an iteration technique, sufficient conditions are derived for the global stability of the disease-free planar equilibrium and the positive equilibrium. Numerical examples are carried out to illustrate the analytical results.

scholarly journals Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator

2009 ◽  
Vol 2009 ◽  
pp. 1-24
Author(s):  
Xiao Zhang ◽  
Rui Xu ◽  
Qintao Gan
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Prey System ◽  
Comparison Argument ◽  
Theoretical Results ◽  
Iteration Technique

A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.

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