Optimal strategies of the age-specific vaccination and antiviral treatment against influenza

Abstract

Influenza, caused by any of several human influenza viruses, is a highly contagious respiratory disease and it produces millions of cases worldwide. Vaccination and antiviral treatment are two main biomedical interventions for curtailing influenza spread. In this paper, an age-structured SVIR influenza model is used to take account for the efficacy of vaccination and antiviral treatment. Next, the stability of the disease-free equilibrium is captured by analyzing the root distributions of the characteristic equation and the existence of the endemic equilibrium is established by employing a generalized fixed point theorem. Moreover, the consideration of the availability of medical resources is settled as an optimal control problem to investigate the cost-effective interventions for the guidelines of optimal policy selection. Numerical simulations show that the outcomes of optimal control are characterized by the cost of control strategies, age structured of hosts and the different measures of influenza intervention. As a result of consequences, we recommend projecting vaccination at the early period and the implement of therapy at the entire infectious course, to slow down or eradicate influenza transmission.