OPTIMAL CONTROL OF INFLUENZA A DYNAMICS IN THE EMERGENCE OF A TWO STRAIN

This paper examines the influenza spread model by considering subpopulation, vaccination, resistance to analgesic/antipyretic drugs + nasal decongestants. Based on the studied model are determined, non-endemic, endemic stability points and the basic reproduction number. In the model studied, control is given in an effort to prevent contact of individuals infected with influenza and susceptible (u1), and control treatment for infected individuals in an effort to accelerate the recovery of infected individuals (u2). In the numerical simulation, using the control u1 the number of infected individuals subpopulation decreased compared to that without control. The number of individual recovered subpopulations using the u2 control increased more than that without the control

Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number, Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lower Rc to a critical value Rc∗ for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza