The impact of imported cases on the persistence of contagious diseases

A model based on cellular automata to estimate the social isolation impact on COVID-19 spreading in Brazil

“…Instead of using deterministic state transitions, the Probabilistic Cellular Automata (PCA) is more suitable for epidemiological studies [1] , [2] , [45] . Accordingly, it has been used for studying migratory movements on the persistence of contagious disease [5] , [16] , the impact of the time delay in the spreading of a disease based on SEIR model [44] , the adaptation of cellular automata for using real population density maps [18] , and disease infection in groups of individuals [37] . Also, for large homogeneous and well-mixed populations, Ordinary Differential Equations (ODE) can be interpreted as a mean-field approximation of the PCA model [4] , [32] , [42] .…”

The influence of immune individuals in disease spread evaluated by cellular automaton and genetic algorithm

“…The states of all individuals are simultaneously updated in the end of each time step. Similar epidemic models based on probabilistic CA were already proposed [23] , [28] , [29] , [30] ; however, this is the first one that takes into consideration the role of immune individuals in the spreading of a contagious disease.…”

A note on the impact of a behavioral side-effect of vaccine failure on the spread of a contagious disease

“…The basic reproduction number of this model is defined as: because implies (and, consequently, the disease is eradicated). This expression can be rewritten as: with: In the absence of vaccination, that is, for and , is the basic reproduction number, as deduced in other works ( Ferraz and Monteiro (2019) ; Schimit and Monteiro, 2009 ).…”

“…For and , the system converges to the endemic steady-state given by: with , , and . For and , Ferraz and Monteiro (2019) had already shown that the endemic attractor is: …”