Dynamics Modeling as a Weapon to
Defend Ourselves Against Threats from
Infectious Diseases and Bioterrorist
Attacks
Hulin Wu, Ph.D., Professor
Director, Center for Biodefense Immune Modeling
Chief, Division of Biomedical Modeling and Informatics
Department of Biostatistics & Computational Biology
University of Rochester Medical Center
SAMSI, February 25, 2011
Outline
• Introduction: Impact of Infectious Diseases to
Public Health
• Dynamic Modeling for HIV
• Dynamic Modeling for Influenza
• Conclusions and Discussions
• Acknowledgement
SARS Pandemic
November 1, 2002-July 31, 2003
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•
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Total Cases: 8096
Death: 774
Death rate: 9.6%
29 countries/regions
USA: 27 cases (no death)
Bird Flu (H5N1) Epidemics in Human
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Total Cases: 285
Death: 170
Death Rate: 59.6%
12 countries/regions
Flu Pandemics: History
• 1918 Spanish flu (H1N1) pandemic: kill
20-100 million people worldwide
• 1957 Asian Flu (H2N2): 1-4 million
infections worldwide, 69,800 deaths in
the US
• 1968 Hong Kong Flu (H3N2): 500,000
infections worldwide, 33,000 deaths in
the US
An Emergency Hospital for Influenza Patients
Annual Influenza Epidemics around the World
• 5-15% of the population affected
• 3-5 million cases of severe illness
• 250,000-500,000 deaths around the
world
Current Estimates of the Yearly Disease
Burden of Influenza in the US
Deaths 40,000
Hospitalizations 100,000
Illnesses 40,000,000
Direct costs ($) 4,000,000,000
Indirect costs ($) - 8,000,000,000
Global HIV/AIDS Epidemics: 2006 Update
Global HIV/AIDS Epidemics: 2006 Update
Global HIV/AIDS Epidemics: 2006 Update
New HIV Infection Rate in 2006
• 8 infections per minute
• 458 infections per hour
Defend Ourselves: Why and How to Use
Mathematics/Statistics as a Weapon?
• Understand pathogenesis of
infection by infectious agents
• Identify therapeutic targets for
intervention
• Design and evaluate the effects of
treatments and other
intervention/prevention strategies
Example: HIV/AIDS Modeling
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1st AIDS case: reported in late 1970s
AIDS virus: discovered in 1983, named HTLV
AIDS virus renamed as HIV in 1986
HIV dynamics models in late 1980s: Merrill
1987; Mclean 1988; Anderson and May 1989;
Perelson 1989
• HIV dynamics models for clinical studies:
David Ho and Alan Perelson (Nature 1995;
Science 1996; Nature 1997)
• My research in HIV dynamics modeling: 1997-
Ho et al, Nature 1995
Ho et al., Nature 1995
• 20 HIV-1 infected patients
• A new antiviral drug: a protease
inhibitor, ABT-538 (Ritonavir)
• Observations: Viral load declined
exponentially in 2 weeks
Ho et al., Nature 1995
Ho et al., Nature 1995
• Tap-Tank Model
dV / dt  P  cV
• Solution with perfect treatment P=0
ct
V (t )  V0e
or
logV (t )  logV0  ct
• Fit a linear regression model
Y (t )  log V0  ct  
c: viral clearance rate
1/c: Mean life-span of HIV virus
ln(2/c): Half-life of HIV virus
Ho et al., Nature 1995
• Estimate of c: 0.34 (range 0.21 to
0.54)
• Half-life of HIV virus: 2.1 (range1.3
to 3.3) days
• Daily production and clearance
rate of HIV virus: 0.68x10^9 (range
0.05 to 2.07x10^9) virions
Perelson et al. and Ho, Science 1996
• A more complicated model
dT * / dt  kVI   T *
dVI / dt  cVI
dVNI / dt  N T * cVNI
• Solution
Y  VI  VNI  V0e
 ct
cV0
c

[
(e  t  e  ct )   te  ct ]  
c  c 
• Clinical data: 5 HIV patients
Perelson et al. and Ho, Science 1996
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Estimate of c: 3.07
Estimate of δ: 0.49
Half-life of virus: 0.24 (about 6 hours).
Half-life of infected cells: 1.55 days
Perelson et al. and Ho, Nature 1997
• Short-lived infected cells: t1/2=1.1 days
• Long-lived inected cells: t1/2=14.1 days
• Latently infected cells: t1/2=8.5 days
My Research: HIV and Influenza
• HIV/AIDS: Use differential equation
models to study antiretroviral treatment
effects and treatment strategies in
HIV/AIDS research
• Influenza: Use differential equation
models to study immune response to
influenza infections and vaccinations
Dynamic Models for AIDS Treatment
• HIV Viral Dynamic Model in Vivo
• Viral fitness is related to antiviral drug efficacy
• Correlate the lab data to clinical data via the
proposed model
Influenza Project
• Center for Biodefense Immune Modeling: funded
by NIH from 2005-2015 with $21.9 million in total
• To develop mathematical models and computer
simulation tools to simulate immune response to
influenza virus
• To design and conduct experiments to validate
the mathematical models and simulation tools
• To expect that our modeling and simulation tools
can help to rapidly design drugs or vaccines to
fight against new and possibly engineered
viruses
A Complex Dynamic System for Influenza Infection:
Lee et al 2009 (J. of Virology)
6/26/09 Annual Meeing
6/2/10
Annual Meeting

Lung Compartment Sub-Model
d
 dt E p   E E p   EPV

d *
*
*
 E p   EPV  k E EPTE (t )   E* E p
 dt
d
*
 dt V    EP  cV V  kVGVAG (t )  kVM VAM (t )

Lung Compartment Sub-Model
Collected data
10
Viral Titer (log10)
8
6
4
2
0
0
5
10
15
Days
Fig 1. HKX31 EID50/ml titers per
murine lung
Fig 2. Cytokine secreting CD8+ T
cells per murine lung
Lung Compartment Sub-Model
Collected data
Fig 3. Smoothed data for IgG and IgM pg/ml murine serum
6/26/09 Annual Meeting
Model Fitting Results
Estimation Result Summary
– The CTL effect: 6.4x10-5/day. Shorten the half-life
of infected cells from 1.16 days to 0.59 days in
average.
– The death rate of infected cells due to effects other
than CTL is 0.16/day which is 26% of the death rate
during the first 5 days
– Antibody effect: IgM dominates the clerance of viral
particles with a rate about 4.4/day. Shorten the halflife from 4 hours to 1.8 minutes in average
– Antibody IgG: not significant
– The clearance rate of viral particles due to factors
other than antibody effect: very small.
Immune Response Kinetics: Useful
• Identify antiviral drug and vaccine
targets
• Understand virulent viruses and their
properties
• Prepareness
DEDiscover
Software tool for developing, exploring, and applying
differential equation models.
Key Features:
• ODE & DDE Models
• “Real-time” interactive simulation
• Data fitting (Estimation)
• Clean, Cross-platform GUI
• High Quality Plots
• Ver 2.5b: freely available
https://cbim.urmc.rochester.edu/software/dediscover
2010-06-02
CBIM DEDiscover Software
42
Conclusions and Discussions
• Efficiently fight against infectious diseases
and bioterrorism:
– Need global effort with efficient collaborations and
communications
– Need efficient collaborations and communications
among inter-disciplinary scientists
– Need long-term effort and huge resources
• Use any weapons available to defend
ourselves including mathematics, computer
and statistics
• Dynamics modeling: an important weapon
• Can we defend ourselves?
Acknowledgments
• NIAID/NIH grant R01 AI 055290: AIDS Clinical Trial
Modeling and Simulations
• NIAID/NIH grant N01 AI50020: Center for Biodefense
Immune Modeling
• NIAID/NIH grant P30 AI078498: Developmental Center
for AIDS Research
• NIAID/NIH grant R21 AI078842: Analysis of Differential
Resistance Emergence Risk for Differential Treatment
Applications
• NIAID/NIH grant RO1 AI087135: Estimation Methods for
Nonlinear ODE Models in AIDS Research