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

Abstract

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,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math>. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lower<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math>to a critical value<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow><mml:mrow><mml:mi>∗</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math>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.