The local and global stability of the disease free equilibrium in a co infect...iosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This presentation, tailored for municipalities, covers the following items: determining your target audience; website basics in 2015; how to drive Web traffic; and keeping engaged with your audience.
In this file, you can ref resume materials for pricing specialist such as pricing specialist resume samples, pricing specialist resume writing tips, pricing specialist cover letters, pricing specialist interview questions with answers…
The local and global stability of the disease free equilibrium in a co infect...iosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This presentation, tailored for municipalities, covers the following items: determining your target audience; website basics in 2015; how to drive Web traffic; and keeping engaged with your audience.
In this file, you can ref resume materials for pricing specialist such as pricing specialist resume samples, pricing specialist resume writing tips, pricing specialist cover letters, pricing specialist interview questions with answers…
An analytic study of the fractional order model of HIV-1 virus and CD4+ T-cel...IJECEIAES
In this article, we study the fractional mathematical model of HIV-1 infection of CD4+ T-cells, by studying a system of fractional differential equations of first order with some initial conditions, we study the changing effect of many parameters. The fractional derivative is described in the caputo sense. The adomian decomposition method (Shortly, ADM) method was used to calculate an approximate solution for the system under study. The nonlinear term is dealt with the help of Adomian polynomials. Numerical results are presented with graphical justifications to show the accuracy of the proposed methods.
Eur. J. Immunol. 2015. 45 3107–3113 Immunity to infectionDOIBetseyCalderon89
Eur. J. Immunol. 2015. 45: 3107–3113 Immunity to infectionDOI: 10.1002/eji.201545940 3107
SHORT COMMUNICATION
Gut commensal microbes do not represent a dominant
antigenic source for continuous CD4+ T-cell activation
during HIV-1 infection
Kathrin Zimmermann1, Sonia Bastidas1, Leandra Knecht1,
Herbert Kuster2, Stephan R. Vavricka4, Huldrych F. Günthard2,3
and Annette Oxenius1
1 Institute of Microbiology, ETH Zurich, Zurich, Switzerland
2 Division of Infectious Diseases and Hospital Epidemiology, University Hospital Zurich,
University of Zurich, Zurich, Switzerland
3 Institute of Medical Virology, University of Zurich, Zurich, Switzerland
4 Division of Gastroenterology and Hepatology, Triemli Hospital, Zurich, Switzerland
Chronic immune activation is a hallmark of HIV-1 infection; specifically, the activation
of T cells has predictive value for progression to AIDS. The majority of hyperactivated
T cells are not HIV-specific and their antigenic specificities remain poorly understood.
Translocation of gut luminal microbial products to systemic sites contributes to chronic
immune activation during HIV-1 infection, but how it affects (TCR-dependent) immune
activation remains elusive. We hypothesized that gut luminal antigens foster activation
of CD4+ T cells with specificities for commensal bacterial antigens, thereby contribut-
ing to the pool of activated CD4+ T cells in the circulation of HIV-1 infected individu-
als. To test this hypothesis, we quantified the frequencies of gut microbe-specific CD4+
T cells by cytokine production upon restimulation with selected gut commensal microbial
antigens. Contrary to our hypothesis, we did not observe increased but rather decreased
frequencies of gut microbe-specific CD4+ T cells in HIV-1 infected individuals compared
to healthy controls. We conclude that the increased activation status of circulating CD4+
T cells in HIV-1 infected individuals is not driven by CD4+ T cells with specificities for
commensal bacterial antigens.
Keywords: Gut microbe-specific CD4+ T-cell responses · IBD and HIV-1 associated enteropathy
· Microbial translocation · Systemic immune activation
�Additional supporting information may be found in the online version of this article at thepublisher’s web-site
Introduction
Chronic activation of the immune system is a major determinant
of progression to AIDS [1] and particularly the level of hyperac-
tivated T cells is considered as best prognostic marker for disease
Correspondence: Dr. Annette Oxenius
e-mail: [email protected]
progression [2]. HIV-1 infection and replication is the main driv-
ing force of persistent, pathological level of T-cell activation [1, 3]
but HIV-1 specific T cells account for only a small fraction of acti-
vated T cells [4–6], implicating substantial “bystander” activation.
Multiple mechanisms are considered to contribute to the genesis
of such extensive immune activation, many of them are related to
HIV-1 associated immunodeficiency [7, 8], su ...
Determination of Average HIV Replication in the Blood Plasma Using Truncated ...paperpublications3
Abstract: Many statistical and computational models have been developed to investigate the complexity of HIV dynamics in the immune response. Most of the models described the viral replication as a system of differential equation, where the solution of parameters is not easy to obtain. A model of HIV replication where infected cells undergo through a truncated logistic distribution is proposed. An infected cell is modelled as an individual entity with certain states and properties. Three simulation approaches are used for implementing the model, conditional distribution, truncated population mean approaches and sample mean. Simulation results give insights about the details of HIV replication dynamics inside the cell at the protein level. Therefore the model can be used for future studies of HIV intracellular replication. It will also promote better understanding of the HIV/AIDS transmission dynamics, the study will also add to the existing body of knowledge on mathematical application in the field of epidemiology.
A very brief & concise ppt. for HIV... Includes a video from YouTube explaining the Replication cycle of HIV. {actually was a class project ;)}. Hope you people like it.
Here's the link to the video: https://www.youtube.com/watch?v=RO8MP3wMvqg
I appreciate any answer. Thank you. For each of the following descri.pdfamiteksecurity
I appreciate any answer. Thank you. For each of the following description!) formulate a
mathematical model as a system of differential equations. In each case give a suitable
compartment diagram and define any parameters or symbols that you introduce that were not
mentioned as part of the question. Consider a model for the spread of a disease where lifelong
immunity is attained after catching the disease. The susceptibles are continuously vaccinated at a
per-capita rate mu against the disease. Develop differential equations for the number of
susceptibles S(t). the number of infectives I(t). the number vaccinated V(t) and the number
recovered. R(t). assuming all who recovered from the infection become immune for life. The
infectious disease Dengue fever is spread by infected mosquitoes that transmit the disease to
humans when they bite susceptible humans. Similarly, when a susceptible mosquito bites an
infected human the mosquito becomes infected Assume that humans cannot directly infect other
humans nor infected mosquitoes infect other mosquitoes. Let Sm(t) and Im(t) denote the number
of susceptible and infected mosquitoes respectively and let S h(t) and I h(t) denote the member of
susceptible and infected humans. Assume that there are no birth or deaths of humans over the
time-scale of interest but that there is a per-capita birth-rate of mosquitoes 6 and per-capita death
rate of mosquitoes of a. Also, assume that humans are infected for a period of gamma-1 and then
recover with immunity. Mosquitoes do not recover. (Note: typically gamma-1 is about. 2 weeks
for dengue fever).
Solution
The number of Vaccinated people (V(t)) is a simple one.
dV/dt = mu * S(t), where S(t) is the number of susceptable people.
A certain percentage of the people who need to be vaccinated are vaccinated every year, and this
will slow down as less people need to be vaccinated.
Susceptable people are decreasing over time, once you have been vaccinated, become sick, or
recover you are set for life.
S(t) = 1 - V(t) - R(t) - I(t)
The growth of the infective population depends on how infective the disease is, but it is also
dependant on how many people can be infected still. Let\'s say every infective person infects
beta percent of other vulnerable people, and they recover x days later.
dI/dt = [beta * I(t) * S(t)] - I(t-x)
The number of recovered people will follow the number of infective people but unlike infective
people they remain recovered
dR/dt = I(t-x)
All of these equations use a total population size of one, you are modelling the percentage of the
population that has fallen under these conditions. Eventually, the equations should reach these
final end conditions when t = infinity:
S(t) = 0, V(t) + R(t) = 1, and I(t) = 0.
Part two is just using these equations and applying them..
Modeling the Effect of Variation of Recruitment Rate on the Transmission Dyna...IOSR Journals
In this Paper, the effect of the variation of recruitment rate on the transmission dynamics of
tuberculosis was studied by modifying an existing model. While the recruitment rate into the susceptible class of
the existing model is constant, in our modified model we used a varying recruitment rate. The models were
analyzed analytically and numerically and these results were compared. The Disease Free Equilibrium (DFE)
state of the existing model was found to be
,0,0,0
, the DFE of the modified model was found to be
( ,0,0,0) * S where * S is arbitrary. While all the eigenvalue of the existing model are negative, one of the
eigenvalues of the modified model is zero. The basic reproduction number o R of both models are established to
be the same. The numerical experiments show a gradual decline in the infected and exposed populations as the
recruitment rates increase in both models but the decline is more in the modified model than in the existing
model. This implies that eradication will be achieved faster using the model with a varying recruitment rate.
An analytic study of the fractional order model of HIV-1 virus and CD4+ T-cel...IJECEIAES
In this article, we study the fractional mathematical model of HIV-1 infection of CD4+ T-cells, by studying a system of fractional differential equations of first order with some initial conditions, we study the changing effect of many parameters. The fractional derivative is described in the caputo sense. The adomian decomposition method (Shortly, ADM) method was used to calculate an approximate solution for the system under study. The nonlinear term is dealt with the help of Adomian polynomials. Numerical results are presented with graphical justifications to show the accuracy of the proposed methods.
Eur. J. Immunol. 2015. 45 3107–3113 Immunity to infectionDOIBetseyCalderon89
Eur. J. Immunol. 2015. 45: 3107–3113 Immunity to infectionDOI: 10.1002/eji.201545940 3107
SHORT COMMUNICATION
Gut commensal microbes do not represent a dominant
antigenic source for continuous CD4+ T-cell activation
during HIV-1 infection
Kathrin Zimmermann1, Sonia Bastidas1, Leandra Knecht1,
Herbert Kuster2, Stephan R. Vavricka4, Huldrych F. Günthard2,3
and Annette Oxenius1
1 Institute of Microbiology, ETH Zurich, Zurich, Switzerland
2 Division of Infectious Diseases and Hospital Epidemiology, University Hospital Zurich,
University of Zurich, Zurich, Switzerland
3 Institute of Medical Virology, University of Zurich, Zurich, Switzerland
4 Division of Gastroenterology and Hepatology, Triemli Hospital, Zurich, Switzerland
Chronic immune activation is a hallmark of HIV-1 infection; specifically, the activation
of T cells has predictive value for progression to AIDS. The majority of hyperactivated
T cells are not HIV-specific and their antigenic specificities remain poorly understood.
Translocation of gut luminal microbial products to systemic sites contributes to chronic
immune activation during HIV-1 infection, but how it affects (TCR-dependent) immune
activation remains elusive. We hypothesized that gut luminal antigens foster activation
of CD4+ T cells with specificities for commensal bacterial antigens, thereby contribut-
ing to the pool of activated CD4+ T cells in the circulation of HIV-1 infected individu-
als. To test this hypothesis, we quantified the frequencies of gut microbe-specific CD4+
T cells by cytokine production upon restimulation with selected gut commensal microbial
antigens. Contrary to our hypothesis, we did not observe increased but rather decreased
frequencies of gut microbe-specific CD4+ T cells in HIV-1 infected individuals compared
to healthy controls. We conclude that the increased activation status of circulating CD4+
T cells in HIV-1 infected individuals is not driven by CD4+ T cells with specificities for
commensal bacterial antigens.
Keywords: Gut microbe-specific CD4+ T-cell responses · IBD and HIV-1 associated enteropathy
· Microbial translocation · Systemic immune activation
�Additional supporting information may be found in the online version of this article at thepublisher’s web-site
Introduction
Chronic activation of the immune system is a major determinant
of progression to AIDS [1] and particularly the level of hyperac-
tivated T cells is considered as best prognostic marker for disease
Correspondence: Dr. Annette Oxenius
e-mail: [email protected]
progression [2]. HIV-1 infection and replication is the main driv-
ing force of persistent, pathological level of T-cell activation [1, 3]
but HIV-1 specific T cells account for only a small fraction of acti-
vated T cells [4–6], implicating substantial “bystander” activation.
Multiple mechanisms are considered to contribute to the genesis
of such extensive immune activation, many of them are related to
HIV-1 associated immunodeficiency [7, 8], su ...
Determination of Average HIV Replication in the Blood Plasma Using Truncated ...paperpublications3
Abstract: Many statistical and computational models have been developed to investigate the complexity of HIV dynamics in the immune response. Most of the models described the viral replication as a system of differential equation, where the solution of parameters is not easy to obtain. A model of HIV replication where infected cells undergo through a truncated logistic distribution is proposed. An infected cell is modelled as an individual entity with certain states and properties. Three simulation approaches are used for implementing the model, conditional distribution, truncated population mean approaches and sample mean. Simulation results give insights about the details of HIV replication dynamics inside the cell at the protein level. Therefore the model can be used for future studies of HIV intracellular replication. It will also promote better understanding of the HIV/AIDS transmission dynamics, the study will also add to the existing body of knowledge on mathematical application in the field of epidemiology.
A very brief & concise ppt. for HIV... Includes a video from YouTube explaining the Replication cycle of HIV. {actually was a class project ;)}. Hope you people like it.
Here's the link to the video: https://www.youtube.com/watch?v=RO8MP3wMvqg
I appreciate any answer. Thank you. For each of the following descri.pdfamiteksecurity
I appreciate any answer. Thank you. For each of the following description!) formulate a
mathematical model as a system of differential equations. In each case give a suitable
compartment diagram and define any parameters or symbols that you introduce that were not
mentioned as part of the question. Consider a model for the spread of a disease where lifelong
immunity is attained after catching the disease. The susceptibles are continuously vaccinated at a
per-capita rate mu against the disease. Develop differential equations for the number of
susceptibles S(t). the number of infectives I(t). the number vaccinated V(t) and the number
recovered. R(t). assuming all who recovered from the infection become immune for life. The
infectious disease Dengue fever is spread by infected mosquitoes that transmit the disease to
humans when they bite susceptible humans. Similarly, when a susceptible mosquito bites an
infected human the mosquito becomes infected Assume that humans cannot directly infect other
humans nor infected mosquitoes infect other mosquitoes. Let Sm(t) and Im(t) denote the number
of susceptible and infected mosquitoes respectively and let S h(t) and I h(t) denote the member of
susceptible and infected humans. Assume that there are no birth or deaths of humans over the
time-scale of interest but that there is a per-capita birth-rate of mosquitoes 6 and per-capita death
rate of mosquitoes of a. Also, assume that humans are infected for a period of gamma-1 and then
recover with immunity. Mosquitoes do not recover. (Note: typically gamma-1 is about. 2 weeks
for dengue fever).
Solution
The number of Vaccinated people (V(t)) is a simple one.
dV/dt = mu * S(t), where S(t) is the number of susceptable people.
A certain percentage of the people who need to be vaccinated are vaccinated every year, and this
will slow down as less people need to be vaccinated.
Susceptable people are decreasing over time, once you have been vaccinated, become sick, or
recover you are set for life.
S(t) = 1 - V(t) - R(t) - I(t)
The growth of the infective population depends on how infective the disease is, but it is also
dependant on how many people can be infected still. Let\'s say every infective person infects
beta percent of other vulnerable people, and they recover x days later.
dI/dt = [beta * I(t) * S(t)] - I(t-x)
The number of recovered people will follow the number of infective people but unlike infective
people they remain recovered
dR/dt = I(t-x)
All of these equations use a total population size of one, you are modelling the percentage of the
population that has fallen under these conditions. Eventually, the equations should reach these
final end conditions when t = infinity:
S(t) = 0, V(t) + R(t) = 1, and I(t) = 0.
Part two is just using these equations and applying them..
Modeling the Effect of Variation of Recruitment Rate on the Transmission Dyna...IOSR Journals
In this Paper, the effect of the variation of recruitment rate on the transmission dynamics of
tuberculosis was studied by modifying an existing model. While the recruitment rate into the susceptible class of
the existing model is constant, in our modified model we used a varying recruitment rate. The models were
analyzed analytically and numerically and these results were compared. The Disease Free Equilibrium (DFE)
state of the existing model was found to be
,0,0,0
, the DFE of the modified model was found to be
( ,0,0,0) * S where * S is arbitrary. While all the eigenvalue of the existing model are negative, one of the
eigenvalues of the modified model is zero. The basic reproduction number o R of both models are established to
be the same. The numerical experiments show a gradual decline in the infected and exposed populations as the
recruitment rates increase in both models but the decline is more in the modified model than in the existing
model. This implies that eradication will be achieved faster using the model with a varying recruitment rate.
1. Three-Component Model
of HIV with
Sensitivity Analysis
December 10th, 2014
by
Dustin Burchett and Alyssa Mandarino
Colorado School of Mines
Abstract
HIV spread in the body can be modeled using the three-component model. The
three variables involved are uninfected T-cells, infected T-cells, and virus cells.
Six parameters are in these equations. They are λ which is the growth rate
of T-cells, µ is the T-cell death rate, k is the infection rate, δ is the infected
cell death rate, p is the virus production rate, and c is the viral clearance rate.
Sensitivity analysis was performed on the model to see which parameter of the
six, when changed, changes the virus count the most. The results of this project
show that the infection rate affects the virus count the greatest. Some current
medical treatment of HIV involve decreasing the infection.
2.
3. 1
Human immunodeficiency virus (HIV) affects a hosts immune system. To
fully understand the model some biological background will be discussed. The
immune system distinguishes between cells and foreign invaders in an organism.
It is prompted to respond by foreign substances called antigens. Once the
immune system finds antigens in the blood they are labeled by a macrophage;
which is found in white blood cells to identify infection sites in the body. At
this point helper T-cells (a lymphocyte called Thymus cells) sends out a signal
to get the B-cell (another lymphocyte) to come and produce antibodies for the
specific antigen. Lymphocytes are white blood cells and identified as either B-
cells or T-cells. The antibodies signal to other immune system cells to come
and destroy it as well as the antigen. Eventually, the immune system rests [3].
HIV is spread through sexual contact or by contact of infected blood. HIV
cells are considered foreign and are attacked by the hosts immune system ini-
tially; however, some virus cells manage to infect T-cells. This is done by the
virus changing then integrating its DNA into the DNA of the T-cell. It enters
the cell and inputs its DNA into the nucleus. Once that is accomplished the
viral DNA then forces the T-cell to replicate the viral DNA. The viral DNA will
manufacture into more virus cells and eventually the T-cell bursts in a process
called cytolysis. When the cell bursts it spreads more virus cells into the blood
stream to infect other T-cells. What can be seen upon infection is that T-cell
count will drop significantly due to the fact that they are becoming infected
cells. As more virus cells enter the blood stream T-cells will continue to drop
until they level off at a significantly lower value than before infection.
A current model called the three-component model represents the spread of
HIV from cell to cell inside the host. The variables in this system of equations
are T, I, and V, respectively representing uninfected T-cells count, infected T-
cells count, and virus cells count. The system is:
dT
dt
= λ − µT − kTV
dI
dt
= kTV − δI
dV
dt
= pI − cV
The parameters involved are λ which is the T-cell growth rate, µ is the T-cell
death rate, k is the infection rate or the contact rate between virus cells and
T-cells, δ is the infected T-cell death rate, p is the virus production rate, and c is
the viral clearance rate or the burst rate of the infected T-cell during cytolysis.
The initial conditions used were T0 = 1000, I0 = 0, and, V0 = 50 [2].
The two equilibrium points calculated are (T1, I1, V1) = λ
µ , 0, 0 and (T2, I2, V2) =
cδ
pk , λ
δ − µc
kp , pλ
cδ − µ
k [2]. The first point, (T1, I1, V1), is known as viral extinc-
tion because the infected and virus cell counts go to zero. The second point,
(T2, I2, V2), is known as viral persistence because the virus is still present within
the host as well as infected cells. Despite the parameters being independent of
4. 2
each other, it was calculated that the parameters must follow the relationship
c < kpλ
δµ to maintain positive equilibrium points. If this condition is not met the
system levels off to the viral extinction point. This model accommodates this
scenario.
The goal of this project was to determine which of the parameters is the most
sensitive, in turn this could help with treatments to target a certain aspect of
the infection process. The effect on the virus count was observed. To test which
parameter effects the system the greatest sensitivity analysis was conducted.
To quantitatively show how parameters affect the system the time it took for
the virus count to reach one of two equilibria was recorded for a multitude of
parameter values. An = 0.1 was picked so when the virus count was within
of its equilibrium point, which was determined by the parameter values, the
time value was recorded and called t ,i; with i representing an index.
To make sure that most parameter combinations were observed, a random set
of parameters were chosen. Four of the five parameters were then held constant
and t ,i was recorded for each individual value, over the range of the remaining
parameter not being held constant (look at Table1 to see all parameter ranges).
Only five parameters are being manipulated because c always equals 3. This
process was done 1000 times checking the range of the same parameter each
time. A histogram of t ,i was plotted.
Now to test the sensitivity of all the parameters, the ranges were normalized
to [-1, 1]. This allows the parameters to be studied without units. This was a
transformation represented by zi = τ(xi) with xi being the original range value
randomly selected, zi is the normalized value, and τ is the transformation. Least
squares was then used to fit the linear model t ,i ≈ ˆu0 + ˆu1z1 + · · · + ˆu5z5. The
ˆu values are weights to the linear model and those were plotted against the
parameters. This gives sensitivity of each parameter to the system. The weight
lie on the [-1, 1] range therefore a parameter with weight close to zero does not
affect the system greatly; however, a weigh near -1 or 1 has a significant effect
on the system. The sufficient summary plot plots t ,i versus ˆui. This shows us
the relationship between the normalized random parameters and t ,i. In other
words, how changes in the parameters effect t ,i.
In terms of this model, it was shown that k was the only parameter that
affects the system significantly. This can be observed. Looking at Graph4 of
the weights, ˆu, versus the parameters it shows that ˆu = −1 at k. µ, k, δ, and
p do not change the system. λ shows some sensitivity because the ˆu at λ does
not equal exactly 0. It is close enough to 0 that the effect cause by changes in λ
can be ignored and the effects of k can be focused on. Essentially, the sufficient
summary plot, Graph5, is t versus k. When comparing the change λ has on the
system in Graph2 and the change k has on the system in Graph1 it is clear that
k changes the system more than λ. This means that if effective HIV treatments
are to be implemented they should limit the contact between virus cells and
uninfected T-cells.
For current treatments today, it is extremely common to take more than
one medication which stops HIV production at different stages of development.
Each medication is put into a class describing at what point the medication stops
5. 3
the virus replication. Nucleoside/Nucleotide Reverse Transcriptase Inhibitors
(NRTIs) is a class that involves blocking the use of the enzyme necessary to make
copies of the viral DNA. The Non-Nucleoside Reverse Transcriptase Inhibitors
(NNRTIs) is very similar to NRTIs but it just prevents the enzyme from working
properly. Protease Inhibitors (PIs) prevents the viral DNA that has already
been replicated from being split into smaller pieces that then become virus
cells[3]. It can be noticed, that all of these classes described involve the HIV
already infecting the T-cell. There is one class called Entry/Fusion Inhibitors
that prevent the HIV cells from attaching to healthy T-cells receptors. These
medications can target both virus cells as well as T-cells[1]. The sensitivity
analysis on this model supports the idea of expanding treatment in Entry/Fusion
Inhibitors. Unfortunately, only two treatment drugs are in this class and two
more are being tested for use[1]. Of the 30 drugs in the market this is not
significant.
Using the previously derived three-component model, this project argues
that the most sensitive parameter in this system of equation representing HIV
within the body is the infection rate of virus cells on healthy T-cells. Since
this parameter is mathematically the most sensitive this means that if scientists
wish to decrease the virus count they should look in the direction of medication
that changes the contact rate of T-cells and HIV cells.
6. Growth Media
Parameters Biological Process Minimum Mean Value Maximum Units
λ T-cell growth rate 0.043 0.1089 0.2 µL−1
day−1
µ T-cell death rate 0.0043 0.01089 0.02 day−1
k Infection rate 0.00019 0.001179 0.0048 µL−1
day−1
δ Infected T-cell death rate 0.13 0.3660 0.8 day−1
p Virus production rate 98 1427 7100 day−1
c Viral clearance rate 3 3 3 day−1
Table 1: range of parameters
7. Figure 1: Plot of T, I , and V with k being the variable that changes
Figure 2: Plot of T, I , and V with λ being the variable that changes
8. Figure 3: Histogram of λ
Figure 4: Showing that k is the most sensitive parameter
10. Bibliography
[1] ”Entry Inhibitors (including Fusion Inhibitors).” Entry Inhibitors (in-
cluding Fusion Inhibitors). N.p., 16 Sept. 2011. Web. 09 Dec.
2014.<http://www.aidsmeds.com/archive/EIs_1627.shtml>
[2] Jones, Eric, Peter Roemer, Mrinal Raghupathi, and Stephen
Pankavich. Analysis and the Simulation of the Three-Component
Model of HIV Dynamics (n.d.): 90-105. Web. 12 Nov.
2014.<https://www.siam.org/students/siuro/vol7/S01269.pdf>
[3] ”Stages of HIV Infection.” Stages of HIV Infection. N.p., n.d. Web. 19 Oct.
2014.<http://www.aids.gov/hiv-aids-basics/just-diagnosed-with-
iv-aids/hiv-in-your-body/stages-of-hiv/>
Thanks to Stephen Pankavich for help with the three-component model as
well as Paul Constantine for help with the sensitivity analysis.