Seasonal Treatment of an Infectious Disease is a Social Driver of Sustained Oscillations in the Disease incidence

Autores

  • O. Osuna
  • J. G. Villavicencio Pulido Universidad Autónoma Metropolitana

DOI:

https://doi.org/10.5540/tcam.2021.022.02.00279

Palavras-chave:

Seasonal treatment rate, periodic orbit, Leray-Schauder degree, SIRS models, reproduction number

Resumo

We analyze a seasonal $SIR$ model that assumes a periodic treatment rate. Using the Leray-Schauder degree theory, we prove that model shows periodic solutions. This result shows that sustained oscillations in the incidence of the disease are related to the periodic application of a treatment against the disease. So, we can say that the periodic application of treatment can be considered a seasonal driver of the sustained oscillations.

Biografia do Autor

J. G. Villavicencio Pulido, Universidad Autónoma Metropolitana

Departamento de Ciencias Ambientales.

Profesor-Titular C.

Referências

G. Pappas, I. J. Kiriaze, and M. E. Falagas, “Insights into infectious disease in the era of hippocrates,” International Journal of Infectious Diseases, vol. 12, pp. 347–350, 2008.

. Altizer et al., “Seasonal and the dynamics of infectious diseases,” Ecology Letters, vol. 9, pp. 467–484, 2006.

S. F. Dowell, “Seasonal variation in host susceptibility and cycles of certain infectious diseases,” Emerg. Infect, vol. 7, pp. 369–373, 2001.

N. C. Grassly and C. Fraser, “Seasonal infectious diseases epidemiology,” Proceedings of the Royal Society B, vol. 273, pp. 2541–2550, 2006.

J. Dushoff, J. B. Plotkin, S. A. Levin, and D. J. D. Earn, “Dynamical resonance can account for seasonality of influenza epidemics,” Proc. Natl Acad. Sci. USA, vol. 101, pp. 16915–16916, 2004.

D. Fishman, “Seasonality of infectious diseases,” Ann. Rev. Public Health, vol. 28, pp. 127–143, 2007.

D. G. Williams and C. Dye, “Infectious disease persistence when transmission varies seasonally,” Mathematical Biosciences, vol. 145, pp. 77–88, 2012.

G. Katriel, “Existence of periodic solutions for the periodically forced sir

model,” Journal of Mathematical Sciences, vol. 201,3, pp. 335–342, 2014.

R. J. Nelson, G. E. Demas, S. L. Kelin, and L. J. Kriegsfeld, Seasonal patterns of stress, immune function and disease. New York: Cambridge University Press, 2002.

I. of Medicine, “The threat of pandemic influenza: Are we ready?,” 2005.

R. H. Borse, S. S. Shrestha, A. E. Fiore, C. Y. Atkins, J. A. Singleton, C. Furlow, and M. I. Meltzer, “Effects of vaccine program against pandemic influenza a(h1n1) virus, united states,” Emerging Infectious Diseases, vol. 19(3), pp. 439–448, 2013.

P. V. den Driessche and J. Watmough, “Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002.

R. M. Anderson and R. M. May, Infectious diseases of humans: dynamics and control. Oxford: Oxford University Press, 1991.

D. C. Lee, J. D. Chidambaram, T. C. Porco, and T. M. Lietman, “Seasonal effects in the elimination of trachoma,” Am. J. Trop. Med. Hyg., vol. 72(4), pp. 468–470, 2005.

W. P. Glezen, “Prevention and treatment of seasonal influenza,” N. Engl. Med., vol. 359, pp. 2579–2585, 2008.

Downloads

Publicado

2021-06-28

Como Citar

Osuna, O., & Villavicencio Pulido, J. G. (2021). Seasonal Treatment of an Infectious Disease is a Social Driver of Sustained Oscillations in the Disease incidence. Trends in Computational and Applied Mathematics, 22(2), 279–289. https://doi.org/10.5540/tcam.2021.022.02.00279

Edição

v. 22 n. 2 (2021)

Seção

Artigo Original

Licença

Direitos Autorais

Autores de artigos publicados no periódico Trends in Computational and Applied Mathematics mantêm os direitos autorais de seus trabalhos. O periódico utiliza a Atribuição Creative Commons (CC-BY) nos artigos publicados. Os autores concedem ao periódico o direito de primeira publicação.

Propriedade Intelectual e Termos de uso

O conteúdo dos artigos é de responsabilidade exclusiva dos autores. O periódico utiliza a Atribuição Creative Commons (CC-BY) nos artigos publicados. Esta licença permite que os artigos publicados sejam reutilizados sem permissão para qualquer finalidade, desde que o trabalho original seja corretamente citado.

O periódico encoraja os Autores a autoarquivar seus manuscritos aceitos, publicando-os em blogs pessoais, repositórios institucionais e mídias sociais acadêmicas, bem como postando-os em suas mídias sociais pessoais, desde que seja incluída a citação completa à versão do website da revista.