A Rule-based Model for a Stochastic Simulation of a Zombie Outbreak Felipe Nu˜ nez 1 , Cesar Ravello 1 , Hector Urbina 1 and Tomas Perez-Acle 1,2,3 1 Computational Biology Lab (DLab), Center for Mathematical Modeling (CMM) Facultad de Ciencias F´ ısicas y Matem´ aticas, Universidad de Chile 2 Fundaci´ on Ciencia para la Vida 3 Centro Interdisciplinario de Neurociencia de Valpara´ ıso Introduction Zombies are fictitious elements gathered from our collective imagination that have attracted much attention during the last years, becoming prominent in books, movies, music and, more recently, video games. They represent an object that generates chaos and shows similarities with events of disease outbreaks at a large scale, leading to a state of catastrophe, affecting people both physically and emotionally. Many models exists to describe the spread of diseases and the case of zombies is no exception, as demonstrated by a previous contribution that presented a simple model based on differential equations [1], very close to classic epidemiology descriptions. Later on, Crossley et al [2] elaborated on this model by translating it, almost directly without further improvements, to an agent-based stochastic model (ABSM). An ABSM to simulate a zombie outbreak that considers the heterogeneity of the subjects is an important step forward to include relevant features commonly overlooked in simpler models. However, the heterogeneity of the subjects should be encompassed with an univocal and unequivocal way to define every subject, dealing at the same time with the combinatorial explosion that emerges from complex dynamical systems. It is then natural to describe and simulate the dynamics of a zombie infection by using a highly descriptive and comprehensive tool such as the Kappa language [3]. By using Kappa, the system can be easily modeled on the premises of the Gillespie’s Stochastic Simulation Algorithm (SSA) [4]. The system is defined as a mixture of agents moving randomly in a given space, generating collisions between them that can lead to reactions expressed as Kappa rules. The modified SSA algorithm determines if there is any ensemble in the mixture that matches with any rule and executes it, making the corresponding changes in the quantities of agents, much alike to an stoichiometric equation. Considering the philosophical point of view that organisms have no intrinsic purpose [5, 6] and that at a certain scale, the behavior of individuals follows patterns beyond themselves, is that we propose a rule-based model to produce a stochastic simulation of a zombie outbreak. The basic unit of our model is a fictitious element -as far as we know- described in many tales through history, as an undead human being that, through various methods, has risen from a cataleptic state to one of pseudo-life, lacking a will of its own. Between the many legends around this being, its origin can be traced to the voodoo cult in which a dead man could be raised by a wizard, turning him into his slave. However, the actual and more spread concept, is the one made famous by the films of George A. Romero, among others, in which a zombie is a human being affected by a contagious disease that turns him into an almost mindless, roaming being with an insatiable hunger for human flesh. However, those films are also related to our work in more indirect ways, as zombies in those films represent a critic element against society in aspects such as discrimination [7] and consumerism [8] as the main driving forces of people’s behavior, which turns them into mindless cattle, once again the principle that the behavior of the masses is governed by general rules. The Model Following the presented stereotype, we can define a zombie Z as the vector of a disease, being a person that has manifested its symptoms and is capable of transmitting it to other susceptible individuals S. The actual mechanism of contagion is usually defined by three states [7–9]. The first stage is the infected I , representing the incubation period characterized by a short asymptomatic phase followed by a rapid decay of the state of 1