Qualitative Analysis of an influenza model with biomedical interventions

Human influenza is an annual public health concern almost globally with considerable societal health care expenses, reduction in affected individual’s productivity and loss of life, especially during the winter season. We propose an extension of the work in [1,2] in order to investigate the impact of biomedical interventions (treatment and vaccination) in a population, taking into consideration the effects of the population pre-existing and waning immunity. Explicit expression of critical treatment thresholds are derived in the context of drug-resistance (with and without drug resistance and seeding of resistant strain infection). Furthermore, critical conditions underlying the appearance of a second wave over a period of months to years are derived in terms of pre-existing and waning immunity. Qualitative analysis of the model show that both the disease-free and endemic equilibria are globally asymptotically stable under appropriate conditions and this precludes any possibility of the phenomenon of backward bifurcation where both the disease-free and endemic equilibria co-exist. These results provide critical conditions for competitive existence of both strains. Numerical simulations for representative set of parameter values (from the literature or assumed) are provided to support the analytical results. When the resistant strain has a good fitness cost, the impact of treatment is significant under a critical threshold of antiviral administration due to the emergence of de novo resistance. Finally, concurrently applying both treatment and vaccination could help mitigate the spread of an influenza epidemic outbreak than singly applying each control measure.