# American Institute of Mathematical Sciences

2008, 5(3): 523-537. doi: 10.3934/mbe.2008.5.523

## Modeling the rapid spread of avian influenza (H5N1) in India

 1 Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India

Received  February 2008 Revised  February 2008 Published  June 2008

Controlling the spread of avian bird flu has become a challenging tasks for Indian agriculture and health administrators. After the first evidence and control of the virus in 2006, the virus attacked five states by January 2008. Based on the evidence of rapid spread of the avian bird flu type H5N1 among the Indian states of Maharashtra, Manipur, andWest Bengal, and in the partially affected states of Gujarat and Madhya Pradesh, a model is developed to understand the spread of the virus among birds and the effect of control measures on the dynamics of its spread. We predict that, in the absence of control measures, the total number of infected birds in West Bengal within ten and twenty days after initial discovery of infection were 780,000 and 2.1 million, respectively. When interventions are introduced, these values would have ranged from 65,000 to 225,000 after ten days and from 16,000 to 190,000 after twenty days. We show that the farm and market birds constitute the major proportion of total infected birds, followed by domestic birds and wild birds in West Bengal, where a severe epidemic hit recently. Culling 600,000 birds in ten days might have reduced the current epidemic before it spread extensively. Further studies on appropriate transmission parameters, contact rates of birds, population sizes of poultry and farms are helpful for planning.
Citation: Arni S.R. Srinivasa Rao. Modeling the rapid spread of avian influenza (H5N1) in India. Mathematical Biosciences & Engineering, 2008, 5 (3) : 523-537. doi: 10.3934/mbe.2008.5.523
 [1] Lesia V. Baranovska. Pursuit differential-difference games with pure time-lag. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1021-1031. doi: 10.3934/dcdsb.2019004 [2] Louis D. Bergsman, James M. Hyman, Carrie A. Manore. A mathematical model for the spread of west nile virus in migratory and resident birds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 401-424. doi: 10.3934/mbe.2015009 [3] Sophia R-J Jang, Hsiu-Chuan Wei. On a mathematical model of tumor-immune system interactions with an oncolytic virus therapy. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021184 [4] Zongmin Yue, Fauzi Mohamed Yusof. A mathematical model for biodiversity diluting transmission of zika virus through competition mechanics. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021235 [5] Riane Hajjami, Mustapha El Jarroudi, Aadil Lahrouz, Adel Settati, Mohamed EL Fatini, Kai Wang. Dynamic analysis of an $SEIR$ epidemic model with a time lag in awareness allocated funds. Discrete & Continuous Dynamical Systems - B, 2021, 26 (8) : 4191-4225. doi: 10.3934/dcdsb.2020285 [6] Antonio Magaña, Alain Miranville, Ramón Quintanilla. On the time decay in phase–lag thermoelasticity with two temperatures. Electronic Research Archive, 2019, 27: 7-19. doi: 10.3934/era.2019007 [7] Anna Chiara Lai, Paola Loreti. Self-similar control systems and applications to zygodactyl bird's foot. Networks & Heterogeneous Media, 2015, 10 (2) : 401-419. doi: 10.3934/nhm.2015.10.401 [8] Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479 [9] Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707 [10] Cecilia Cavaterra, Denis Enăchescu, Gabriela Marinoschi. Sliding mode control of the Hodgkin–Huxley mathematical model. Evolution Equations & Control Theory, 2019, 8 (4) : 883-902. doi: 10.3934/eect.2019043 [11] Urszula Ledzewicz, Behrooz Amini, Heinz Schättler. Dynamics and control of a mathematical model for metronomic chemotherapy. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1257-1275. doi: 10.3934/mbe.2015.12.1257 [12] Zhuangyi Liu, Ramón Quintanilla. Time decay in dual-phase-lag thermoelasticity: Critical case. Communications on Pure & Applied Analysis, 2018, 17 (1) : 177-190. doi: 10.3934/cpaa.2018011 [13] Jose-Luis Roca-Gonzalez. Designing dynamical systems for security and defence network knowledge management. A case of study: Airport bird control falconers organizations. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1311-1329. doi: 10.3934/dcdss.2015.8.1311 [14] Mario Lefebvre. A stochastic model for computer virus propagation. Journal of Dynamics & Games, 2020, 7 (2) : 163-174. doi: 10.3934/jdg.2020010 [15] Elamin H. Elbasha. Model for hepatitis C virus transmissions. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1045-1065. doi: 10.3934/mbe.2013.10.1045 [16] Nicola Bellomo, Youshan Tao. Stabilization in a chemotaxis model for virus infection. Discrete & Continuous Dynamical Systems - S, 2020, 13 (2) : 105-117. doi: 10.3934/dcdss.2020006 [17] A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909 [18] V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model. Networks & Heterogeneous Media, 2006, 1 (4) : 621-637. doi: 10.3934/nhm.2006.1.621 [19] Shuo Wang, Heinz Schättler. Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1223-1240. doi: 10.3934/mbe.2016040 [20] Colette Calmelet, John Hotchkiss, Philip Crooke. A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1449-1464. doi: 10.3934/mbe.2014.11.1449

2018 Impact Factor: 1.313