Publication:
Análisis de brotes epidémicos

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2018
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Abstract
A detailed explanation of an epidemiological mathematical paper (”Numerical study of SARS epidemic model with the inclusion of diffusion in the system”) is carried out. Theoretical background is provided when needed, as well as its practical application to the case of study. Calculations, graphics and numerical results are also included.
Description
UCM subjects
Matemáticas (Matemáticas) , Análisis matemático , Enfermedades infecciosas
Unesco subjects
12 Matemáticas , 1202 Análisis y Análisis Funcional , 3205.05 Enfermedades Infecciosas
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[1] A.Naheed, M.Singh y D. Lucy, Numerical study of SARS epidemic model with the inclusion of diffusion in the system Applied Mathematics and Computation 22, (2014) 480–498. [2] A. Chakraborty, M. Singh, D. Lucy, P. Ridland, Predator–prey model with prey-taxis and diffusion, Math. Comput. Model. 46, (2007) 482–498. [3] G. Chowell, P.W. Fenimore, M.A. Castillo-Garsow, C. Castillo-Chavez, SARS outbreak in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism, J. Theor. Biol. 224, (2003) 1–8. [4] O. Diekmann, J.A.P. Heesterbeek, J.A.J. Metz, C. Castillo- Chavez, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28, (1990) 365–382. [5] P. Driessche Van den, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002) 29–48. [6] H.W. Hethcote, The mathematics of infectious diseases, SIAM 42 (2000) 599–653. [7] Abba B. Gumel, Modelling strategies for controlling SARS outbreaks, R. Soc. 271 (2004) 2223–2232. [8] N. Sapoukhina, Y. Tyutyunov, A. Arditi, The role of prey-taxis in biological control, Am. Nat. 162 (2003) 61–76. [9] Md. Samsuzzoha, M. Singh, D. Lucy, Numerical study of an influenza epidemic model with diffusion, Appl. Math. Comput. 217 (7) (2010) 3461–3479. [10] Md. Samsuzzoha, M. Singh, D. Lucy, A Study on numerical solutions of epidemic models (Ph.D. thesis), Swinburne University of Technology, Australia, 2012. [11] <http://www.who.int/csr/sars/en>, 2003 [12] R.A. Horn, C.R. Johnson, Topics in Matrix Analysis Cambridge University, Cambridge, 1991. [13] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos Springer, Berlin, 1990. [14] O. Diekmann, J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation Wiley, New York, 1999. [15] M. Singh, A. Easton, I. Kozlova, A numerical study of the sprucebudworm reaction-diffusion equation with hostile boundaries, Natural Research Modelling 13 (2000) 535–549. [16] Murray, J. D., Mathematical biology Springer, New York, 1993. [17] Willem Hundsdorfer, Jan Verwer Numerical Solution of Time- Dependent Advection-Diffusion-Reaction Equations Volume 33, Springer, 2003. [18] Steven H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Westview Press, 2001. [19] Fred Brauer, Mathematical Epidemiology Springer, 2008. [20] Hirsch, Morris W., Differential Equations, Dynamical Systems, and an Introduction to Chaos Elsvier, 2003. [21] Crank, J, Nicolson, P A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of Heat Conduction Type (1947) [22] Abraham Berman, Robert J. Plemmons Nonnegative Matrices in the Mathematical Sciences 1979. [23] Jacobson, N., Basic Algebra I, San Francisco: W. H. Freeman, 1974.
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https://hdl.handle.net/20.500.14352/20931
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Trabajos Fin de Grado (TFG) y Diplomas de Estudios Avanzados (DEA)