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. 2018 Aug 29:2018:2434560.
doi: 10.1155/2018/2434560. eCollection 2018.

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

Caroline W Kanyiri  1 , Kimathi Mark  2 , Livingstone Luboobi  3
Affiliations

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

Caroline W Kanyiri et al. Comput Math Methods Med. .

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, 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.

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Figures

Figure 1
Figure 1
Global circulation of influenza viruses from 2016 to 2017.
Figure 2
Figure 2
Global circulation of influenza viruses from 2017 to week 24 of 2018.
Figure 3
Figure 3
Excess mortality due to influenza for the U.S. population aged 65 years and above.
Figure 4
Figure 4
Schematic diagram showing population flow between different epidemiological classes.
Figure 5
Figure 5
Endemic equilibrium points of the two-strain influenza model.
Figure 6
Figure 6
Force of infection, λ1, versus control reproduction number, Rcw.
Figure 7
Figure 7
Force of infection, λ2, versus control reproduction number, Rcr.
Figure 8
Figure 8
Relationship between reproduction numbers and drug resistance.
Figure 9
Figure 9
Effect of drug resistance on IR class.
Figure 10
Figure 10
Effect of drug resistance on Iw class.
Figure 11
Figure 11
I R individuals with no vaccination.
Figure 12
Figure 12
I w individuals with no vaccination.
Figure 13
Figure 13
I R individuals with vaccination.
Figure 14
Figure 14
I w individuals with vaccination.
Figure 15
Figure 15
Effect of βw on individuals infected with wild-type strain.
Figure 16
Figure 16
Effect of βr on individuals infected with resistant strain.
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