Mathematical Modeling of Bird Flu Propagation Urmi Ghosh-Dastidar New York City College of Technology City University of New York December 1, 2007

Bird Flu Propagation Model Assumptions Disease initiates from Birds Birds may spread the disease to birds and humans Humans cannot transmit the disease Birds never recover from the disease; death is eventual (SI propagation model) Humans may recover from the disease or die; if recovered  permanent recovery  immunity (SIR propagation model)

Terminologies H(t) = Total number of humans at a given time t B(t) = Total number of birds at a given time t H s = Susceptible humans, B s = Susceptible birds H i = Infectious humans, B i = Infectious Birds H r = Recovered Humans H(t) = H s + H r + H i at any given time B(t) = B s + B i at any given time S H = H s /H; I H = H I /H S B = Bs/B; I B = B I /B The number of contacts per unit time by an infectious bird with the susceptible humans S H  H = (H s /H)  H where the average number of contacts (assuming that this contact is sufficient to transmit the infection) of an infectious bird with a human per unit time =  H

Bird Flu Model

Equilibrium Points

Conclusion Irrespective of the initial infected population, the extent of disease propagation depends on the average contact number. The model is robust with respect to its parameters  H or a H ; in every case the model actually reaches equilibrium points E5 and E6 respectively if either of the followings are true: or Human-to-human transmission will be considered in future. Thank You!