Dynamics Modeling as a Weapon to Defend Ourselves Against Threats from

Infectious Diseases and Bioterrorist Attacks

SAMSI, February 25, 2011

Hulin Wu, Ph.D., ProfessorDirector, Center for Biodefense Immune Modeling

Chief, Division of Biomedical Modeling and Informatics

Department of Biostatistics & Computational BiologyUniversity of Rochester Medical Center

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

• Total Cases: 8096

• Death: 774

• Death rate: 9.6%

• 29 countries/regions

• USA: 27 cases (no death)

Bird Flu (H5N1) Epidemics in Human

• 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

40,000100,000

40,000,0004,000,000,0008,000,000,000

Deaths -Hospitalizations -Illnesses -Direct costs ($) -Indirect costs ($) -

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

• 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

• Solution with perfect treatment P=0

• Fit a linear regression model

c: viral clearance rate

1/c: Mean life-span of HIV virus

ln(2/c): Half-life of HIV virus

/dV dt P cV

0 0( ) log ( ) logctV t V e or V t V ct

0( ) logY t V ct

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

• Solution

• Clinical data: 5 HIV patients

* / *

/

/ *

I

I I

NI NI

dT dt kV T

dV dt cV

dV dt N T cV

00 [ ( ) ]ct t ct ct

I NI

cV cY V V V e e e te

c c

Perelson et al. and Ho, Science 1996

• 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

** * *

*

( )

( ) ( )

p E p P

p P E P E pE

P V VG G VM M

dE E E V

dtdE E V k E T t E

dtdV E c V k VA t k VA t

dt

Lung Compartment Sub-Model

Fig 1. HKX31 EID50/ml titers per murine lung

0

2

4

6

8

10

0 5 10 15Days

Vir

al T

iter

(lo

g10

)

Collected data

Fig 2. Cytokine secreting CD8+ T cells per murine lung

6/26/09 Annual Meeting

Lung Compartment Sub-Model

Fig 3. Smoothed data for IgG and IgM pg/ml murine serum

Collected data

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 half-life 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

42

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

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