Biological Attack Model (BAM) Progress Report March 8 Sponsor: Dr. Yifan Liu Richard Bornhorst Robert Grillo Deepak Janardhanan Shubh Krishna Kathryn Poole

2 Agenda Project Plan Work Breakdown Biological Agent Parameters Assumptions Revisited Preliminary Model Overview Current Modeling Issues

3 Project Plan

4 Work Breakdown 320 of 875 man-hours completed. Ahead of schedule on modeling –End modeling phase by next brief to give an extra week to testing, evaluation, analysis, and recommendations (4 weeks) –Develop early skeleton for final report

5 Biological Agent Parameters Smallpox (β = 3) (d = 30%) –Incubation Period: 7-17 days –Prodrome Period: 2-4 days –Symptomatic Period: 20 days Ebola (β = 1-2) (d = 40%-90%) –Incubation Period: 2-20 days –Prodrome Period: 2-4 days –Symptomatic Period: 6-9 days Viral Encephalitis (β = 3-4) (d = 3%-60%) –Incubation Period: 5-15 days –Prodrome Period: 2-4 days –Symptomatic Period: 7-14 days

6 Assumptions Revisited Attack Assumptions –Single source where a certain number of people are initially exposed –Diseases will be transmitted person to person rather than airborne or food borne –Detected 24 hours after incident (may adjust for future analysis) Population Assumptions –Constant population with no immigration/emigration, births, or deaths that aren’t related to the disease –People in the incubation stage (non-contagious) are considered susceptible in terms of quarantine and treatment since they are not yet known to be infected

7 Assumptions Revisited Quarantine Assumptions –Various percentages of the population are quarantined to analyze effectiveness Isolation of confirmed and suspected cases with vaccination and quarantine of contacts traced to these cases All other quarantine is voluntary confinement –A percentage of the population cannot be quarantined Vaccination and Treatment Assumptions –A percentage of population is already vaccinated (when applicable) –Emergency response and medical staff already vaccinated (if available) –Treatments are available for recovering those that receive it –Vaccination and treatment have no significant side effects –Those in quarantine without symptoms receive available vaccination –Those showing symptoms do not receive vaccination (treatment only)

8 Two Phases First Phase –The spread of the pathogen before detection Initial assumption is detection occurs after 24 hours, but this will be adjusted to analyze the importance of early detection –Only three states during this phase: Susceptible, Infected, Infectious Second Phase –Occurs after outbreak has been identified The status of states at end of first phase provide initial conditions for second phase Containment strategies employed

9 S+Qi1+Qi2+Qs+I1+I2+RN+RT+RD+D = N Track 10 different populations Susceptible S Infected I 1 Infectious I 2 Quarantined Infected Q i1 Quarantined Infectious Q i2 Quarantined Susceptible Q S Recovered Without Treatment R N Recovered With Treatment R T Disabled R D Dead D Preliminary Model Diagram

10 Preliminary Model Parameters Transmission Rate (  Average Incubation Length (  Average Infectious Length (  Disease Mortality Rate (d) Quarantine Rate (q) Tracing Close Contacts of Infectious (  ) Number of Treated Per Day (  ) Treatment Efficacy Period (b) Disability Ratio (g) Total Population (N)

11 Preliminary Model Parameters (Excel snapshot)

12 Example Plot: 10,000 treated per day, 30% Quarantine Rate

13 Example Plot: 10,000 treated per day, No Quarantine

14 Example Plot: 20,000 treated per day, 30% Quarantine Rate

15 Current Modeling Issues Modeling a Coherent Detection Scheme Disease incubation periods vs. appearance of symptoms Arriving at a Balance between Number of States & Reality Risk of Inaccuracy vs. simplification Recovery without treatment, Side effects…. Integrity checks to be built in Containment as a combination of Reducing Contacts and Treatment Resource Allocation Effective Treatment allocation issue Availability of Emergency Responders Effect of varying β due to Intervention efforts Diverse Containment strategies emerging for different diseases More data available on Smallpox than the others Translating results into Information for a Decision Maker Use of percentages of population vs. absolute numbers

16 Questions ?