Competitive exclusion in a multi-strain immuno-epidemiological influenza model with environmental transmission

• Main Authors: Yan-Xia Dang, Xue-Zhi Li, Maia Martcheva
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-01-01
• Series: Journal of Biological Dynamics
• Subjects: Age-since-infection; multi-strain; competitive exclusion; reproduction number; environmental transmission; Lyapunov function
• Online Access: http://dx.doi.org/10.1080/17513758.2016.1217355

In this paper, a multi-strain model that links immunological and epidemiological dynamics across scales is formulated. On the within-host scale, the n strains eliminate each other with the strain having the largest immunological reproduction number persisting. However, on the population scale, we extend the competitive exclusion principle to a multi-strain model of SI-type for the dynamics of highly pathogenic flu in poultry that incorporates both the infection age of infectious individuals and biological age of pathogen in the environment. The two models are linked through the age-since-infection structure of the epidemiological variables. In addition the between-host transmission rate, the shedding rate of individuals infected by strain j and the disease-induced death rate depend on the within-host viral load. The immunological reproduction numbers $ R_j $ and the epidemiological reproduction numbers $ \mathcal {R}_j $ are computed. By constructing a suitable Lyapunov function, the global stability of the infection-free equilibrium in the system is obtained if all reproduction numbers are smaller or equal to one. If $ \mathcal {R}_j $ , the reproduction number of strain j is larger than one, then a single-strain equilibrium, corresponding to strain j exists. This single-strain equilibrium is globally stable whenever $ \mathcal {R}_j>1 $ and $ \mathcal {R}_j $ is the unique maximal reproduction number and all of the reproduction numbers are distinct. That is, the strain with the maximal basic reproduction number competitively excludes all other strains.