Data Assimilation Methods in Parameter Estimation: An Application to Tuberculosis Transmission Model IIT Mandi, Himachal Pradesh Pankaj Narula and Arjun Bhardwaj Supervisors: Dr. Sarita Azad Dr. Ankit Bansal International Conference on Mathematical Techniques in Engineering Applications (ICMTEA 2013)
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Bayesian Estimation of Reproductive Number for Tuberculosis in India
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Data Assimilation Methods in Parameter Estimation: An Application to Tuberculosis Transmission Model IIT Mandi, Himachal Pradesh Pankaj Narula and Arjun Bhardwaj Supervisors: Dr. Sarita Azad Dr. Ankit Bansal
International Conference on Mathematical Techniques in Engineering
Applications (ICMTEA 2013)
Outline
Epidemiology of Tuberculosis (TB)
Model Formulation and Parameters
Research Interests
Previous Work on TB
Estimation Methods
Results
Epidemiology of Tuberculosis
TB is one of the most widespread infectious diseases, and a leading cause of global mortality.
Particularly, TB in India accounts for 25% of the world’s incident cases.
RNTCP is being implemented by Government of India in the country with DOTS strategy.
The SIR Epidemic Model
S
Susceptible: can catch the disease
I
Infectious: have caught the disease and can spread it to susceptible
R
Recovered: have recovered from the disease and are immune.
dS dt
= – b S I
dI dt
= b S I – γI
dR dt
= γ I
S + I + R = 1
Parameters of the Model
= The infection rate
= The Removal rate
= Fraction of infectious persons.
Basic reproduction number obtained as:
Average secondary number of infections caused by an infective in total susceptible population. An epidemic occur if .
Fraction of population needs to be vaccinated 1 − 1/R0.
0
pR
b
bp
0 1R
Model Formulation
SILS Model of TB
Recovery rate is assumed to be 0.85.
Aim is to estimate β and p.
( )
(1 )
dS ISI L
dt N
dI pISI tL
dt N
dL p ISI tL
dt N
b
b
b
Research Interests
Mathematical models, deterministic or statistical, are important tools to understand TB dynamics and analyse voluminous data collected by various agencies like WHO, RNTCP.
Challenge is to accurately estimate model parameters.
Parameters like infection rate measure the disease burden and evaluate the measures for control.