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

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• 作者：Alhaji Cherif^a ; ^b ; ^{cherif@asu.edu" class="auth_mail" title="E-mail the corresponding author} ; Janet Dyson^c ; Philip K. Maini^b ; Sunetra Gupta^d
• 关键词：Age-structured epidemic model ; Stability analysis ; Antigenically diverse diseases ; Strain community structures ; Principle of competitive exclusion
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：34
• 期：Complete
• 页码：275-315
• 全文大小：1568 K

文摘

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 behaviours 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 R₀<1${\mathcal{R}}_0<1$, all strains go to extinction. When R₀>1${\mathcal{R}}_0>1$, 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 co-existence 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 behaviours (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.