Steady State Solution and Stability of an Age-Structured MSIQR Epidemic Model

References

[1] N. M. Ferguson, C. A. Donnelly and R. M. Anderson, “Transmission Intensity and Impact of Control Policies on the Foot and Mouth Epidemic in Great Britain,” Nature, Vol. 413, No. 6855, 2001, pp. 542-548.

[2]
M. Lipsitch, T. Cohen, B. Cooper, J. M. Robins, S. Ma, L. James, G. Gopalakrishna, S. K. Chew, C. C. Tan, M. H. Samore, D. Fisman and M. Murray, “Transmission Dynamics and Control of Severe Acute Respiratory Syndrome,” Science, Vol. 300, No. 5627, 2003, pp. 1966- 1970.

[3]
S. Hsu and L. W. Roeger, “The Final Size of a SARS epidemic Model without Quarantine,” Journal of Mathe- matical Analysis and Applications, Vol. 333, No. 2, 2007, pp. 557-566.

[4]
W. O. Kermack and A. G. Mckendrick, “A Contribution to the Mathematical Theory of Epidemics,” Proceedings of the Royal Society of London – Series A, Vol. 115, No. 772, 1927, pp. 700-721.

[5]
S. Riley, “Large-Scale Spatial-Transmission Models of Infectious Disease,” Science, Vol. 316, No. 5829, 2007, pp. 1298-1301.

[6]
P. E. Parham, B. K. Singh and N. M. Ferguson, “Analytic Approximation of Spatial Epidemic Models of Foot and Mouth Disease,” Theoretical Population Biology, Vol. 73, No. 3, 2008, pp. 349-368.

[7]
M. J. Keeling, M. E. J. Woolhouse, D. J. Shaw, L. Matthews, M. Chase-Topping, D. T. Haydon, S. J. Cornell, J. Kappey, J. Wilesmith and B. T. Grenfell, “Dynamics of the 2001 UK Foot and Mouth Epidemic: Stochastic Dispersal in a Heterogeneous Landscape,” Science, Vol. 294, No. 5543, 2001, pp. 813-817.

[8]
H. C. Tuckwell and R. J. Williams, “Some Properties of a Simple Stochastic Epidemic Model of SIR Type,” Mathe- matical Biosciences, Vol. 208, No. 1, 2007, pp. 76-97.

[9]
S. Gao, L. Chen and Z. Teng, “Impulsive Vaccination of an SEIRS Model with Time Delay and Varying Total Population Size,” Bulletin of Mathematical Biology, Vol. 69, No. 2, 2007, pp. 731-745.

[10]
H. W. Hethcode, “The Mathematics of Infectious Diseases,” SIAM Review, Vol. 42, No. 4, 2000, pp. 599-653.

[11]
J. Arino, J. R. Davis, D. Hartley, R. Jordan, J. M. Miller and P. van den Driessche, “A Multi-Species Epidemic Model with Spatial Dynamics,” Mathematical Medicine and Biology, Vol. 22, No. 2, 2005, pp. 129-142.

[12]
F. Hoppensteadt, “An Age Dependent Epidemic Model,” Journal of the Franklin Institute, Vol. 297, No. 5, 1974, pp. 325-333.

[13]
F. Hoppensteadt, “Mathematical Theories of Populations: Demographics,” Genetics and Epidemics, SIAM, Philadelphia, 1975.

[14]
Z. Zhang and J. G. Peng, “A SIRS Epidemic Model with Infection-Age Dependence,” Journal of Mathematical Analysis and Applications, Vol. 331, No. 2, 2007, pp. 1396-1414.

[15]
H. R. Thieme and C. Castillo-Chavez, “How may Infection Age-Dependent Infectivity Affect the Dynamics of HIV/AIDS?” SIAM Journal on Applied Mathematics, Vol. 53, No. 5, 1993, pp. 1447-1479.

[16]
C. M. Kribs-Zaleta and M. Martcheva, “Vaccination Stra- tegies and backward Bifurcation in an Age-since-Infection Structured Model,” Mathematical Biosciences, Vol. 177- 178, 2002, pp. 317-332.

[17]
H. Inaba and H. Sekine, “A Mathematical Model for Chagas Disease with Infection-Age-Dependent Infectivity,” Mathematical Biosciences, Vol. 190, No. 1, 2004, pp. 39- 69.

[18]
B. Fang and X. Li, “Stability of an Age-Structured MSEIS Epidemic Model with Infectivity in Latent Period,” Acta Mathematicae Applicatae Sinica, Vol. 31, No. 1, 2008, pp. 110-125.

[19]
G. B. Webb, “Theory of Nonlinear Age-Dependent Population Dynamics,” CRC Press, Boca Raton, 1985.

[20]
J. Li, Y. C. Zhou, Z. Z. Ma and M. Hyman, “Epidemiological Models for Mutating Pathogens,” SIAM Journal on Applied Mathematics, Vol. 65, No. 1, 2004, pp. 1-23.

[21]
H. W. Hethcotevan and P. den Driessche, “Two SIS Epidemiologic Models with Delays,” Journal of Mathematical Biology, Vol. 40, No. 1, 2000, pp. 3-26.

[22]
W. H. McNeill, “Plagues and Peoples,” Updated Edition, Anchor, Garden City, 1976.

[23]
A. Mandavilli, “SARS Epidemic Unmasks Age-Old Quarantine Conundrum,” Nature Medicine, Vol. 9, No. 5, 2003, p. 487.

[24]
B. Diamond, “SARS Spreads New Outlook on Quarantine Models,” Nature Medicine, Vol. 9, No. 12, 2003, p. 1441.

[25]
Y. H. Hsieh, C. C. King, C. W. Chen, M. S. Ho, S. B. Hsu and Y. C. Wu, “Impact of Quarantine on the 2003 SARS Outbreak: A Retrospective Modeling Study,” Journal of Theoretical Biology, Vol. 244, No. 4, 2007, pp. 729-736.

[26]
L. Sattenspiel and D. A. Herring, “Simulating the Effect of Quarantine on the Spread of the 1918-19 Flu in Central Canada,” Bulletin of Mathematical Biology, Vol. 65, No. 1, 2003, pp. 1-26.

[27]
H. W. Hethcote, Z. E. Ma and S. B. Liao, “Effects of Quarantine in Six Endemic Models for Infectious Diseases,” Mathematical Biosciences, Vol. 180, No. 1, 2002, pp. 141-160.

[28]
C. T. Bauch, J. O. Lloyd-Smith, M. P. Coffee and A. P. Galvani, “Dynamically Modelling SARS and Other Newly Emerging Respiratory Illnesses: Past, Present and Future,” Epidemiology, Vol. 16, No. 6, 2005, pp. 791-801.