Epidemic thresholds in a heterogenous population with competing strains

Among many epidemic models, one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper, we consider the case where all of the strains obey the susceptible-infected-susceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach, we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi—Albert (BA) scale-free networks are in good agreement with the analytical results.

[1]  M Balter,et al.  New HIV Strain Could Pose Health Threat , 1998, Science.

[2]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[3]  Mimmo Iannelli,et al.  Strain replacement in an epidemic model with super-infection and perfect vaccination. , 2005, Mathematical biosciences.

[4]  Chen Zengqiang,et al.  Study of epidemic spreading on scale-free networks with finite maximum dissemination , 2008 .

[5]  Alessandro Vespignani,et al.  Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. , 2003, Physical review letters.

[6]  Ruan Jiong,et al.  Modelling the spread of sexually transmitted diseases on scale-free networks , 2009 .

[7]  Fred Brauer,et al.  The Kermack-McKendrick epidemic model revisited. , 2005, Mathematical biosciences.

[8]  Carlos Castillo-Chavez,et al.  Dynamics of Two-Strain Influenza with Isolation and Partial Cross-Immunity , 2005, SIAM J. Appl. Math..

[9]  Declan Butler,et al.  Swine flu: One killer virus, three key questions , 2009, Nature.

[10]  M. Newman.  Threshold effects for two pathogens spreading on a network. , 2005, Physical review letters.

[11]  M. Small,et al.  Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Alberto d’Onofrio,et al.  A note on the global behaviour of the network-based SIS epidemic model , 2008 .

[14]  C. K. Michael Tse,et al.  Small World and Scale Free Model of Transmission of SARS , 2005, Int. J. Bifurc. Chaos.

[15]  M. Small,et al.  Scale-free distribution of avian influenza outbreaks. , 2007, Physical review letters.

[16]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[17]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[18]  Gavin J. D. Smith,et al.  Origins and evolutionary genomics of the 2009 swine-origin H1N1 influenza A epidemic , 2009, Nature.

[19]  Carlos Castillo-Chavez,et al.  Competitive Exclusion in Gonorrhea Models and Other Sexually Transmitted Diseases , 1996, SIAM J. Appl. Math..

[20]  R. May,et al.  Infection dynamics on scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  N. Konno,et al.  Multi-state epidemic processes on complex networks. , 2005, Journal of theoretical biology.

[22]  C. Dye,et al.  Dynamics and control of the global tuberculosis epidemic , 2000, Current opinion in pulmonary medicine.

[23]  F C Santos,et al.  Epidemic spreading and cooperation dynamics on homogeneous small-world networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Maia Martcheva,et al.  SEROTYPE REPLACEMENT OF VERTICALLY TRANSMITTED DISEASES THROUGH PERFECT VACCINATION , 2008 .

[25]  Lin Wang,et al.  Global Stability of Virus Spreading in Complex Heterogeneous Networks , 2008, SIAM J. Appl. Math..

[26]  Y. P. Zhang,et al.  Study of runaway electron behaviour during electron cyclotron resonance heating in the HL-2A Tokamak , 2009 .

[27]  Akira Sasaki,et al.  The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model , 2002 .