Final epidemic size and optimal control of socio-economic multi-group influenza model

Flu, a common respiratory disease is caused mainly by the influenza virus. The Avian influenza (H5N1) outbreaks, as well as the 2009 H1N1 pandemic, have heightened global concerns about the emergence of a lethal influenza virus capable of causing a catastrophic pandemic. During the early stages of an epidemic a favourable change in the behaviour of people can be of utmost importance. An economic status-based (higher and lower economic class) structured model is formulated to examine the behavioural effect in controlling influenza. Following that, we have introduced controls into the model to analyse the efficacy of antiviral treatment in restraining infections in both economic classes and examined an optimal control problem. We have obtained the reproduction number [Formula: see text] along with the final epidemic size for both the strata and the relation between reproduction number and epidemic size. Through numerical simulation and global sensitivity analysis, we have shown the importance of the parameters [Formula: see text] and [Formula: see text] on reproduction number. Our result shows that by increasing [Formula: see text] , [Formula: see text] and by decreasing [Formula: see text] , [Formula: see text] and [Formula: see text] , we can reduce the infection in both the economic group. As a result of our analysis, we have found that the reduction of infections and their level of adversity is directly influenced by positive behavioural patterns or changes as without control susceptible population is increased by [Formula: see text] , the infective population is decreased by [Formula: see text] and the recovered population is increased by [Formula: see text] in the higher economic group who opted changed behaviour as compared to the lower the economic group (people living with normal behaviour). Thus normal behaviour contributes to the spread and growth of viruses and adds to the hassle. We also examined how antiviral drug control impacts both economic strata and found that in the higher economic strata, the susceptible population increased by [Formula: see text] , the infective population decreased by [Formula: see text] and the recovered population improved by [Formula: see text] as compared to the lower economic group, the susceptible population has increased by [Formula: see text] , the infective population is decreased by [Formula: see text] and the recovered population is improved by [Formula: see text] . Our results enlighten the role that how different behaviour in separate socio-economic class plays an important role in changing the dynamics of the system and also affects the basic reproduction number. The results of our study suggest that it is important to adopt a modified behaviour like social distancing, wearing masks accompanying the time-dependent controls in the form of an antiviral drug’s effectiveness to combat infections and increasing the proportion of the susceptible population.