Sequential Vaccination for Containing Epidemics

The dynamics of infectious diseases spread is crucial in determining their risk and offering ways to contain them. We study sequential vaccination of individuals in networks, where there is a limit on the number of individuals that can be vaccinated every day. Effective allocation of vaccine will play a critical role in preventing the spread and reducing the effects of a future pandemic. We derive methods for calculating upper and lower bounds of the expected number of infected individuals, as well as provide estimates on the number of vaccinations that is needed for containment. We calculate these explicitly on trees, d-dimensional grids, and Erdős Rényi graphs. Finally, we construct a time-dependent budget allocation strategy and demonstrate its superiority over constant budget allocation on real networks following first acquaintance vaccination. Our results provide a principled approach to assess the needed vaccination rate given the social graph topology.

[1]  Ping Wang,et al.  The surviving rate of an infected network , 2010, Theor. Comput. Sci..

[2]  Reuven Cohen,et al.  Efficient immunization strategies for computer networks and populations. , 2002, Physical review letters.

[3]  Tao Zhou,et al.  Vaccination intervention on epidemic dynamics in networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Piet Van Mieghem,et al.  Optimization of network protection against virus spread , 2011, 2011 8th International Workshop on the Design of Reliable Communication Networks (DRCN).

[5]  Zhongyuan Ruan,et al.  Epidemic spreading with information-driven vaccination. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Yiming Yang,et al.  Introducing the Enron Corpus , 2004, CEAS.

[7]  John N. Tsitsiklis,et al.  When Is a Network Epidemic Hard to Eliminate? , 2015, Math. Oper. Res..

[8]  Chengbin Peng,et al.  Epidemic threshold and immunization on generalized networks , 2010 .

[9]  Amin Saberi,et al.  How to distribute antidote to control epidemics , 2010, Random Struct. Algorithms.

[10]  Francisco J. Rodríguez,et al.  The firefighter problem: Empirical results on random graphs , 2015, Comput. Oper. Res..

[11]  Adam Wierman,et al.  Minimizing the Social Cost of an Epidemic , 2011, GAMENETS.

[12]  Joel C. Miller,et al.  Effective vaccination strategies for realistic social networks , 2007 .

[13]  John N. Tsitsiklis,et al.  An efficient curing policy for epidemics on graphs , 2014, 53rd IEEE Conference on Decision and Control.

[14]  Chinwendu Enyioha,et al.  Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks , 2013, 52nd IEEE Conference on Decision and Control.

[15]  Fan Chung Graham,et al.  Distributing Antidote Using PageRank Vectors , 2009, Internet Math..

[16]  Christos Faloutsos,et al.  Graph evolution: Densification and shrinking diameters , 2006, TKDD.