The foundation of the study presented in this article is the logical-linguistic modeling of complex systems with chaotic dynamics that accounts for past experience using available statistical data on the spread of viral epidemic to control the damage and support communications. The study objective is to apply the system analysis for intelligent data processing for predicting the spread of viral epidemics in the context of the Far North and the Arctic, for the assessing the consequences, determining damage and facilitating the decision-making that involves communications among actors of the extensive networks. The results are presented as modeling epidemic and pandemic in complex system with chaotic dynamics. The paper considers the procedure of applying linguistic-combinatorial modeling that represents subtype of logical-linguistic approach to the complex systems with chaotic dynamics for the analysis of the consequences of the development of epidemics by introducing redundant variables in the semantic models of the domain. The procedure is designed for the hardware and software bundle for analysis and monitoring the impact of epidemics in the regions of the Russian Far North and maintain the communications in the dangerous situations of rapidly spreading diseases. The authors provide the rationale for the development of the artificial intelligence center of the Institute of Program Systems of the Russian Academy of Sciences (AIReC PSI RAS) that implements Miracle system to model the systems with chaotic dynamics and high degree of complexity and support communications for solving the problematic situations conditioned by the viral epidemic or pandemic.