Dubey2007 - A mathematical model for the effect of toxicant on the immune system (with toxicant effect) Model2

  public model
Model Identifier
BIOMD0000000905
Short description 
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.
Keywords: Pathogen; Immune Response; Toxicant; Stability.
Format
SBML (L2V4)
Related Publication
  • A mathematical model for the effect of toxicant on the immune system
  • UMA S. DUBEY and BALRAM DUBEY
  • Journal of Biological Systems , 7/ 2007 , Volume 15 , Issue 4 , pages: 473-493 , DOI: 10.1142/S0218339007002301
  • Department of Biological Sciences Department of Mathematics BITS, Pilani – 333 031, India
  • 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.
Contributors
Submitter of the first revision: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan

Metadata information

Curation status
Curated
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Model files
Dubey2007_model2.xml SBML L2V4 representation of Dubey2007 - A mathematical model for the effect of toxicant on the immune system (with toxicant effect) Model2 46.24 KB Preview | Download

Additional files
Dubey2007_model2.cps COPASI version 4.24 (Build 197) representation of Dubey2007 - A mathematical model for the effect of toxicant on the immune system (with toxicant effect) Model2 82.17 KB Preview | Download
Dubey2007_model2.sedml SEDML L1V2 representation of Dubey2007 - A mathematical model for the effect of toxicant on the immune system (with toxicant effect) Model2 2.64 KB Preview | Download

  • Model originally submitted by : Mohammad Umer Sharif Shohan
  • Submitted: Dec 19, 2019 3:29:39 PM
  • Last Modified: Dec 19, 2019 3:29:39 PM
Revisions
  • Version: 2 public model Download this version
    • Submitted on: Dec 19, 2019 3:29:39 PM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000905
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
I

BTO:0005810 		1.0 mmol
T

C894 		1.0 mmol
U 1.0 mmol
P

Microorganism 		1.0 mmol
M 1.0 mmol
Reactions
Reactions Rate Parameters
=> I; P compartment*(mu+b*I*P) mu = 0.04; b = 0.3
=> T compartment*Q0 Q0 = 5.0
=> U; T compartment*theta_0*T theta_0 = 1.2
I => ; P, U compartment*(a*I+n*gamma*I*P+n1*k1*U*I) a = 0.8; gamma = 0.05; n = 0.1; k1 = 0.6; n1 = 0.5
=> P compartment*beta*P beta = 0.5
U => ; I compartment*(delta_1*U+k1*U*I) delta_1 = 0.02; k1 = 0.6
T => compartment*delta_0*T delta_0 = 0.4
M => compartment*alpha0*M alpha0 = 0.1
=> M; P compartment*alpha*P alpha = 2.4
P => ; I compartment*(gamma*I*P+beta0*P*P) beta0 = 0.2; gamma = 0.05
Curator's comment:
(added: 19 Dec 2019, 15:29:03, updated: 19 Dec 2019, 15:29:03)
The model has been encoded in COPASI 4.24 (Build 197) and the figure 7 of the publication has been reproduced using ggplot package in R This must be added that beta values are changed to 0.9,0.7,0.5 to produce the figure. It is the second model with the toxicant from the paper