Modelo compartimental de Covid-19: cobertura de aplicación de pruebas de detección y rapidez de respuesta

Palabras clave: Covid19, cobertura de pruebas de detección, modelo epidemiológico, modelo SIR, brote epidémico


Presentamos un modelo epidemiológico compartimental para la transmisión del virus Covid-19 que denominamos SEIART, que contempla testeo para individuos infectados sintomáticos y asintomáticos. El modelo es una generalización de los modelos clásicos SIR, SEIR y SEIAR, e incluye las clases de individuos infectados sintomáticos testeados y no testeados, así como individuos asintomáticos testeados y no testeados. Mostramos el número reproductivo básico asociado al sistema y exhibimos que decrece con el aumento en las tasas de testeo y de aplicación tanto en las clases de infectados sintomáticos como asintomáticos. Presentamos simulaciones para mostrar que un aumento en las pruebas y una mayor efectividad en las pruebas de aplicación / detección provocan una reducción en la población infectada y en la mortalidad.


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Amazon, J. J., Goh, S. L., and Feigenson, G. W. (2013). Competition between line tension and curvature stabilizes modulated phase patterns on the surface of giant unilamellar vesicles: A simulation study. Phys. Rev. E., 87:022708.

Arfken, G. and Weber, H., editors (2005). Mathematical Methods for Physicists. Elsevier Academic Press.

Ball, P. (2015). Forging patterns and making waves from biology to geology: a commentary on Turing (1952) the chemical basis of morphogenesis. Phil. Trans. R. Soc. B, 370:20140218.

Brigatti, E., Nuñez-López, M., and Oliva, M. (2011). Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction. Eur. Phys. J. B, 81:321.

Brinkmann, F., Mercker, M., Richter, T., and Marciniak-Czochra, A. (2018). Post-Turing tissue pattern formation: Advent of mechanochemistry. PLOS Computational Biology, 14:e1006259.

Capasso, V. and Wilson, R. (1997). Analysis of a reaction-diffusion system modeling man–environment–man epidemics. SIAM J. Appl. Math., 57:327– 346.

Castro-Villarreal, P., Villada-Balbuena, A., Méndez-Alcaraz, J. M., Castañeda-Priego, R., and Estrada-Jiménez, S. (2014). A brownian dynamics algorithm for colloids in curved manifolds. J. Chem. Phys., 140:214115.

Chacón-Acosta, G., Nuñez-López, M., and Pineda, I. (2020). Turing instability conditions in confined systems with an effective position-dependent diffusion coefficient. J. Chem. Phys., 152.

Chaplain, M., Ganesh, M., and Graham, I. (2001). Spatio-temporal pattern for mation on spherical surfaces: numerical simulation and application to solid tumour growth. Journal of Mathematical, 42.

Crank, J. (1980). The Mathematics of Diffusion. Oxford University Press.

do Carmo, M., editor (1976). Differential Geometry of curves and surfaces. Prentice Hall, Inc., New Jersey.

Fuselier, E. and Wright, G. (2013). A high-order kernel method for diffusion and reaction-diffusion equations on surfaces. J. Sci. Comput., 56:535.

Fuseya, Y., Katsuno, H., Behnia, K., and Kapitulnik, A. (2021). Nanoscale Turing patterns in a bismuth monolayer. Nat. Phys., 17:1031–1036.

Gatenby, R. A. and Gawlinski, E. (1996). A reaction-diffusion model of cancer invasion. Cancer Research, 56:5745–5753.

Getzin, S., Yizhaq, H., Bell, B., Erickson, T. E., Postle, A. C., Katra, I., Tzuk, O., Zelnik, Y. R., Wiegand, K., Wiegand, T., and Meron, E. (2016). Disco very of fairy circles in Australia supports self-organization theory. PNAS, 113:3551–3556.

Gierer, A. and Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik, 12:30–39.

Gjorgjieva, J. and Jacobsen, J. (2007). Turing patterns on growing spheres: the exponential case. DCDS Supplements, 2007(Special):436–445.

Krause, A. L., Burton, A. M., Fadai, N. T., and Gorder, R. A. V. (2018). Emer- gent structures in reaction-advection-diffusion systems on a sphere. Phys. Rev. E, 97:042215.

Krause, A. L., Ellis, M. A., and Gorder, R. A. V. (2019). Influence of curva- ture, growth, and anisotropy on the evolution of Turing patterns on growing manifolds. Bull. Math. Biol., 81:759–799.

León-Velasco, D. A. and Chacón-Acosta, G. (2021). Full finite element scheme for reaction-diffusion systems on embedded curved surfaces in R3. Adv. Math. Phys., page 8898484.

Liaw, S., Yang, C., Liu, R., and Hong, J. (2001). Turing model for the patterns of lady beetles. Phys. Rev. E, 64:041909.

Liu, Y. J., Zhu, L., Wang, A., and Wang, B. (2011). Dynamical behavior of an epidemic model. Braz. J. Phys., 41:304–308.

Mimar, S., Juane, M. M., Park, J., Muñuzuri, A. P., and Ghoshal, G. (2019). Turing patterns mediated by network topology in homogeneous active systems. Phys. Rev. E, 99:062303.

Murray, J. D., editor (2003). Mathematical Biology II: Spatial Models and Biomedical Applications. Third Edition, Springer-Verlag, Berlin Heidelberg.

Nampoothiri, S. (2016). Stability of patterns on thin curved surfaces. Phys. Rev. E, 94:022403.

Nuñez-López, M., Chacón-Acosta, G., and Santiago, J. A. (2017). Diffusion-driven instability on a curved surface: Spherical case revisited. Braz. J Phys, 47:231–238.

Plaza, R., Sánchez-Garduño, F., Padilla, P., Barrio, R., and Maini, P. (2004). The effect of growth and curvature on pattern formation. J. Dyn. Diff. Eqs., 16:1093.

Ramakrishnan, N., Kumar, P. S., and Radhakrishnan, R. (2014). Mesoscale computational studies of membrane bilayer remodeling by curvatureinducing proteins. Phys. Rep., 543:1–60.

Sens, P. and Turner, M. S. (2011). Microphase separation in nonequilibrium biomembranes. Phys. Rev. Lett., 106:238101.

Stoop, N., Lagrange, R., Terwagne, D., Reis, P., and Dunkel, J. (2015). Curvature-induced symmetry breaking determines elastic surface patterns. Nature Materials, 14:337–342.

S´ánchez-Garduño, F., Krause, A. L., Castillo, J. A., and Padilla, P. (2019). Turing-Hopf patterns on growing domains: the torus and the sphere. J. Theor. Biol., 481:136–150.

Turing, A. M. (1952). The chemical basis of morphogenesis. Philos. Trans. Roy. Soc., 237:37–72.

Turing, A. M. (1954). Part iii: A solution of the equations morphogenetical for the case of spherical symmetry.

van Meer, G., Voelker, D. R., and Feigenson, G. W. (2008). Membrane lipids: where they are and how they behave. Nat. Rev. Mol. Cell Biol., 9:112–124.

Vandin, G., Marenduzzo, D., Giryachev, A. B., and Orlandini, E. (2016). Correction: Curvature-driven positioning of Turing patterns in phase-separating curved membranes. Soft Matt., 12:3888–3896.

Varea, C., Arago ́n, J., and Barrio, R. (1999). Turing patterns on a sphere. Phys. Rev. E, 60:4588.

Webb, G. F. (1981). A reaction-diffusion model for a deterministic diffusive epidemic. J. Math. Anal. Appl., 84:150–161.

Zhu, L., Yuan, H., Wu, K., Wang, X., Liu, G., Sun, J., Liao, X., and Chen, X. (2021). Curvature-controlled delamination patterns of thin films on spherical substrates. iScience, 24:102616.

Cómo citar
Umedigo-Valdez, M., & Franco-Pérez, L. (2022). Modelo compartimental de Covid-19: cobertura de aplicación de pruebas de detección y rapidez de respuesta. Pädi Boletín Científico De Ciencias Básicas E Ingenierías Del ICBI, 10(Especial), 74-85.