An age-structured multi-strain epidemic model for antigenically diverse infectious diseases: A multi-locus framework

Abstract

The establishment of cross-protective responses and development of immunity within a host exert pressure on pathogens through cross-immunity mediated competition between antigenic forms. In this paper, we incorporate age-specificity in the multi-locus epidemic model used to study the pathogen-specific dynamic behaviors for infectious diseases with diverse co-circulating antigenic types. We establish results on the existence of a unique mild solution, and on the necessary conditions for local stability of the steady-states. In particular, we find that, when the reproductive number R 0 < 1, all strains go to extinction. When R 0 > 1, we show that there exist additional conditions which determine the stability of different types of endemic equilibria, namely weak and strong endemicity, where the weak endemic equilibria correspond to the existence of principle of competitive exclusions of pathogen-specific clusters, while strong endemicity represents the coexistence of all strains. Using numerical simulations, we also show that weak endemic equilibria yield dynamic features in which only one of the clusters containing discrete strain structures (e.g., of minimally, or non-overlapping antigenic types) persists while others go to extinction. For unique strong endemicity, we observe no strain structure, where antigenic types co-exist or exhibit cyclical strain structure with diverse dynamical behaviors (e.g., (quasi-)periodicity, intermittency, chaos). This demonstrates that pathogenic-specific dynamic features are ubiquitous and shows how cross-immunity between antigenic variants shape the maintenance and evolution of strain structures.

Online Social Network Emergency Public Event Information Propagation and Nonlinear Mathematical Modeling

“…The model was also used to examine social network effects to better understand the topological structure of social contact and the impact of its properties. An improved susceptible-infected-susceptible (SIS) epidemic 2 Complexity spreading model is proposed in order to provide a theoretical method to analyze and predict the spreading of diseases [16][17][18][19][20]. This model is based on the following idea: in social networks, the contact probability between nodes is decided by their social distances and their active degrees.…”