A graph cellular automaton with relation-based neighbourhood describing the impact of peer influence on the consumption of marijuana among college-aged youths

Abstract

A novel approach depicting the dynamics of marijuana usage to gauge the effects of peer influence in a school population, is the site of investigation. Consumption of drug is considered as a contagious social epidemic which is spread mainly by peer influences. A relation-based graph-CA (r-GCA) model consisting of 4 states namely, Nonusers (N), Experimental users (E), Recreational users (R) and Addicts (A), is formulated in order to represent the prevalence of the epidemic on a campus. The r-GCA model is set up by local transition rules which delineates the proliferation of marijuana use. Data available in [4] is opted to verify and validate the r-GCA. Simulations of the r-GCA system are presented and discussed. The numerical results agree quite accurately with the observed data. Using the model, the enactment of campaigns of prevention targeting N, E and R states respectively were conducted and analysed. The results indicate a significant decline in marijuana consumption on the campus when a campaign of prevention targeting the latter three states simultaneously, is enacted.

Assessing the Impact of Contact Tracing, Quarantine and Red Zone on the Dynamical Evolution of the Covid-19 Pandemic using the Cellular Automata Approach and the Resulting Mean Field System: A Case study in Mauritius

“…Moreover, the implementation of red zone in a given population points out the dynamic suppression of connections lying outside the red zone. Therefore, in contrast to systems [20] and [21] whereby the connectivity of a given individual is kept fixed, the r-GCA established in the present work has the additional ability to adjust the connectivity of a given cell when red zones are imposed. Accordingly, the r-GCA system set up in [21] is modified in order to embody these features.…”

“…Therefore, in contrast to systems [20] and [21] whereby the connectivity of a given individual is kept fixed, the r-GCA established in the present work has the additional ability to adjust the connectivity of a given cell when red zones are imposed. Accordingly, the r-GCA system set up in [21] is modified in order to embody these features. To date, to the best of our knowledge, this study is the first of its kind whereby the aforementioned features have been considered in a CA system to model the spread of an infectious disease such as the Covid-19 virus in a given environment.…”

“…These neighbourhoods can also be extended using a radius around the reference cell. In the relation-based graph-CA (r-GCA) neighbourhood, the connections of each cell, who are far away but close in the relationship of common friends and cliques amongst others, are considered [21] . Contact network is an essential feature to be assimilated into the mathematical modelling of diseases where social interactions take place over large-scale areas which enhances the measure of infection risk within the community [22] .…”

“…In this model, the relation-based graph CA neighbourhood [21] is employed to simulate the spread of the disease over the given lattice. Fixed boundary conditions are considered, which are randomly chosen using the rand function in the Matlab software, from the states .…”

A symbiosis between cellular automata and dynamic weighted multigraph with application on virus spread modeling

“…This model does not support relational conceptions of space as well as remote transmission of agents or data without intermediaries. On the contrary, by focusing on the interaction between cells through transmission pathways, the adjacency relationship can be represented using graphs or vector layers (in Geospatial Information Science), and even the neighborhood radius can be considered on these structures [29] , [30] , [31] , [32] , [33] . However, providing a communication network between cells in the form of a 0/1 graph allows the modeling of direct communication between two non-adjacent cells, it is not capable of modeling the intensity of communication between cells.…”