# American Institute of Mathematical Sciences

• Previous Article
Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells
• MBE Home
• This Issue
• Next Article
On the mathematical modelling of tumor-induced angiogenesis
February  2017, 14(1): 67-77. doi: 10.3934/mbe.2017005

## Network-based analysis of a small Ebola outbreak

 1 College of Public Health, The Ohio State University, Columbus, OH 43210, USA 2 Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA 3 Department of Mathematics and Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA 4 College of Public Health and Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA

Received  November 06, 2015 Accepted  April 15, 2016 Published  October 2016

Fund Project: This research has been supported in part by the Mathematical Biosciences Institute and the National Science Foundation under grants RAPID DMS-1513489 and DMS-1440386.

We present a method for estimating epidemic parameters in network-based stochastic epidemic models when the total number of infections is assumed to be small. We illustrate the method by reanalyzing the data from the 2014 Democratic Republic of the Congo (DRC) Ebola outbreak described in Maganga et al. (2014).

Citation: Mark G. Burch, Karly A. Jacobsen, Joseph H. Tien, Grzegorz A. Rempała. Network-based analysis of a small Ebola outbreak. Mathematical Biosciences & Engineering, 2017, 14 (1) : 67-77. doi: 10.3934/mbe.2017005
##### References:

show all references

##### References:
The empirical secondary case distribution in the DRC outbreak dataset (neglecting the index case), as given by Maganga et al.[22]
Estimated posterior densities for the parameters of interest for the non-Markovian MCMC sampler. Green line denotes the posterior mean
Final outbreak size distribution based on 20,000 simulations of the branching processes from the posterior parameter distribution. The actual outbreak size of 69 based on the DRC dataset (black line) is shown for comparison
 [1] Ellina Grigorieva, Evgenii Khailov. Determination of the optimal controls for an Ebola epidemic model. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1071-1101. doi: 10.3934/dcdss.2018062 [2] Joanna Tyrcha, John Hertz. Network inference with hidden units. Mathematical Biosciences & Engineering, 2014, 11 (1) : 149-165. doi: 10.3934/mbe.2014.11.149 [3] Jiani Wang, Liwei Zhang. Statistical inference of semidefinite programming with multiple parameters. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1527-1538. doi: 10.3934/jimo.2019015 [4] Arti Mishra, Benjamin Ambrosio, Sunita Gakkhar, M. A. Aziz-Alaoui. A network model for control of dengue epidemic using sterile insect technique. Mathematical Biosciences & Engineering, 2018, 15 (2) : 441-460. doi: 10.3934/mbe.2018020 [5] Oliver J. Maclaren, Helen M. Byrne, Alexander G. Fletcher, Philip K. Maini. Models, measurement and inference in epithelial tissue dynamics. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1321-1340. doi: 10.3934/mbe.2015.12.1321 [6] Evangelos Evangelou. Approximate Bayesian inference for geostatistical generalised linear models. Foundations of Data Science, 2019, 1 (1) : 39-60. doi: 10.3934/fods.2019002 [7] IvÁn Area, FaÏÇal NdaÏrou, Juan J. Nieto, Cristiana J. Silva, Delfim F. M. Torres. Ebola model and optimal control with vaccination constraints. Journal of Industrial & Management Optimization, 2018, 14 (2) : 427-446. doi: 10.3934/jimo.2017054 [8] William Chad Young, Adrian E. Raftery, Ka Yee Yeung. A posterior probability approach for gene regulatory network inference in genetic perturbation data. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1241-1251. doi: 10.3934/mbe.2016041 [9] Shouying Huang, Jifa Jiang. Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate. Mathematical Biosciences & Engineering, 2016, 13 (4) : 723-739. doi: 10.3934/mbe.2016016 [10] Valery Y. Glizer, Vladimir Turetsky, Emil Bashkansky. Statistical process control optimization with variable sampling interval and nonlinear expected loss. Journal of Industrial & Management Optimization, 2015, 11 (1) : 105-133. doi: 10.3934/jimo.2015.11.105 [11] Deena Schmidt, Janet Best, Mark S. Blumberg. Random graph and stochastic process contributions to network dynamics. Conference Publications, 2011, 2011 (Special) : 1279-1288. doi: 10.3934/proc.2011.2011.1279 [12] Dariush Mohamadi Zanjirani, Majid Esmaelian. An integrated approach based on Fuzzy Inference System for scheduling and process planning through multiple objectives. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1235-1259. doi: 10.3934/jimo.2018202 [13] Patrick M. Fitzpatrick, Jacobo Pejsachowicz. Branching and bifurcation. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 1955-1975. doi: 10.3934/dcdss.2019127 [14] Fred Brauer. Some simple epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 1-15. doi: 10.3934/mbe.2006.3.1 [15] Fred Brauer, Zhilan Feng, Carlos Castillo-Chávez. Discrete epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (1) : 1-15. doi: 10.3934/mbe.2010.7.1 [16] T. S. Evans, A. D. K. Plato. Network rewiring models. Networks & Heterogeneous Media, 2008, 3 (2) : 221-238. doi: 10.3934/nhm.2008.3.221 [17] Shuping Li, Zhen Jin. Impacts of cluster on network topology structure and epidemic spreading. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3749-3770. doi: 10.3934/dcdsb.2017187 [18] James M. Hyman, Jia Li. Differential susceptibility and infectivity epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 89-100. doi: 10.3934/mbe.2006.3.89 [19] Julien Arino, Fred Brauer, P. van den Driessche, James Watmough, Jianhong Wu. A final size relation for epidemic models. Mathematical Biosciences & Engineering, 2007, 4 (2) : 159-175. doi: 10.3934/mbe.2007.4.159 [20] Qingming Gou, Wendi Wang. Global stability of two epidemic models. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 333-345. doi: 10.3934/dcdsb.2007.8.333

2018 Impact Factor: 1.313