Modelling and Optimal Control of Influenza Dynamics with Structured Populations Based on Education and Isolation

This paper presents a new mathematical model for the transmission of avian influenza virus dynamics with education-structured susceptible and isolation-structured infectious human populations in the presence of vaccination. Several dynamical systems methodologies are employed to analyse the avian influenza in human-bird interacting populations. The fundamental properties exhibited by the model are assessed through the theory of positivity and boundedness of solutions. The effective reproduction number, Re, that measures the spread potential of the influenza infection is calculated using the next generation matrix approach. Metzler matrix approach and Lyapunov function are employed to investigate the global asymptotic dynamics of the model about its influenza-free and endemic states, respectively. Furthermore, the model is extended to accommodate four time-dependent control interventions, such as public awareness campaign, vaccination, treatment with anti-viral drugs, and birds culling strategy. By applying Pontryagin's maximum principle, the optimal control quadruple are characterized. Specifically, combinations of any three of the control interventions are explored in forestalling the transmission of avian influenza in the population. The findings of the study do not only reveal various parameters of the model to be targeted for prevention and control of the disease, but also show the importance of consolidating control efforts in the fight against the avian influenza disease.