A Markov Chain Approach to Model Reconstruction

A Markov Chain Approach to Model Reconstruction

Valeria Scapini Eduardo Zuñiga

Centro de Investigación en Innovación, Desarrollo Económico y Políticas Sociales (CIDEP), Universidad de Valparaíso, Chile

Complex Engineering Systems Institute (ISCI), Universidad de Chile, Chile

Available online: 
| Citation



Motivated by the fact that Chile is one of the most seismically active countries in the world (located over the ‘Pacific Ring of Fire’), we define a methodology for estimating the cost of housing reconstruction by modelling the occurrence of natural disasters as a Markov chain. Specifically, the states of the chain correspond to the different possible conditions of the housing infrastructure and the transition probabilities represent the possibility of change from one condition to another once the disaster has occurred. We prove that for the case of the 2010 Chilean earthquake, the matrix representing the process admits a stationary state vector. Using this vector, which we interpreted as the portion of time that the chain spends in each state in the long term, we define a cost function associated with total reconstruction. If this cost function is continuous, then this methodology allows policymakers to make decisions when facing the trade-off between current partial reconstruction and future total reconstruction.


earthquake, Markov chain, natural disasters, reconstruction cost


[1] Cereceda, P., Errázuriz, A.M. y Lagos, M. Terremotos y Tsunamis en Chile. Origo Ediciones,Santiago, 2011.

[2] Scapini V. & Zuñiga E., “Conditions of housing infrastructure before the occurrence ofan earthquake” WIT Transactions on Engineering Sciences, Vol. 129, WIT Press, 2020,ISSN 1743-3533.

[3] Pérez, E. & Thompson, P., Natural hazards: Causes and effects: Lesson 2—earthquakes.Prehospital and Disaster Medicine, 9(4), pp. 260–272, 1994. https://doi.org/10.1017/s1049023x00041510

[4] Naghii, M., Public health impact and medical consequences of earthquakes. RevistaPanamericana de Salud Pública, 18, pp. 216–221, 2005. https://doi.org/10.1590/s1020-49892005000800013

[5] Alvarez, G., Ramirez, J., Paredes, L. & Canales, M., Zonas oscuras en el sistema dealarma de advertencia de tsunami en Chile. Ingeniare. Revista Chilena de Ingeniería,18(3), pp. 316–325, 2010. https://doi.org/10.4067/s0718-33052010000300005

[6] Shabnam, N., Natural disasters and economic growth: A review. International Journalof Disaster Risk Science, 5(2), pp. 157–163, 2014. https://doi.org/10.1007/s13753-014-0022-5

[7] U.S. Geological Survey Earthquakes FAQ.

[8] 20 largest earthquakes in the world, USGS, https://www.usgs.gov/natural-hazards/earthquake-hazards/science/20-largest-earthquakes-world, Accessed on: 15 Mar. 2019.

[9] OPS, El terremoto y tsunami del 27 de febrero en Chile: Crónicas y lecciones aprendidasen el sector salud, Organización Panamericana de la Salud, Santiago de Chile,2010.

[10] Mora, S. 10 años del 27-F: El terremoto que remeció y cambió a Chile para siempre.

[Photographer]. Recuperado de https://www.24horas.cl/nacional/10-anos-del-27-f-elterremoto-que-remecio-a-chile-y-para-el-que-nadie-estaba-preparado-3948765

[11] Rojas, J. A 10 años del 27F: El terremoto que cambió la cultura chilena [Photographer].Recuperado de https://www.duna.cl/noticias/2020/02/27/a-10-anos-del-27f-elterremoto-que-cambio-la-cultura-chilena/

[12] Ross, S.M., Stochastic Processes. John Wiley & Sons: New York, 1996.