Stochastic Study using Markov chains for the Transmission of Dengue
DOI:
https://doi.org/10.15359/ru.32-1.7Keywords:
Control, dengue, epidemic, Markov chains, model, probabilityAbstract
Dengue is a viral disease transmitted to humans by bites of the Aedes aegypti mosquito which can lead to different stages of the disease. Dengue has now widely spread in the world and affects millions of people. In this paper, we present a study based on the transition matrix of a homogeneous Markov chain, in which its states coincide with the possible stages a person goes through in the transmission dynamics of Dengue, and the behavior of the entities is observed over time. The paper also proposes a control strategy based on the transcendental probability weight incorporated in the matrix to reduce the impact of the epidemic on the society. The success of the model Markov proposed is that it is complex enough to describe certain nontrivial features of some systems; but, at the same time, it is simple to be analyzed mathematically.
References
Bar, M. E. (2011). El Aedes aegypti y la transmisión del dengue (Tesis doctoral). Facultad de Ciencias Exactas y Naturales, Universidad Nacional del Nordeste, Argentina.
Diekmann, O., & Heesterbeek, J. (2000). Mathematical Epidemiology of Infectious Diseases: Model Building,Analysis and Interpretation. West Sussex: Wiley.
Taylor, M. (1994). An Introduction to stochastic modeling. Michigan: Academic Press.
Trajstman, A. C. (2002). A Markov Chain Model for Newcastle Disease and its Relevance to the Intracerebral Pathogenicity Index. Biometrical Journal, 44(1), 43–57. doi: https://doi.org/10.1002/1521-4036(200201)44:1<43::AID-BIMJ43>3.0.CO;2-3
Tudor, C. (1994). Procesos estocásticos. Aportaciones matemáticas (Serie Texto 2). Mexico: Sociedad Matemática Mexicana.
Yang, H.-C., & Chao, A. (2005). Modeling Animals’ Behavioral Response by Markov Chain Models for Capture–Recapture Experiments. Biometrics, 61(4), 1010–1017. doi: https://doi.org/10.1111/j.1541-0420.2005.00372.x
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