A mathematical model to study resistance and non-resistance strains of influenza

Results in Physics

Khadijah M. Abualnaja¹  M.D. Alsulami²  Hijaz Ahmad³  Isa Abdullahi Baba⁴  Mohamed Altanji⁵ 

[1] Corresponding author.;Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy;Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan;Department of Mathematical Sciences, Bayero University, Kano, Nigeria;University of Jeddah, College of Sciences and Arts at Alkamil, Department of Mathematics, Jeddah, Saudi Arabia;

关键词: Equilibrium points;    Bilinear incidence rate;    Basic reproduction ratio;    Saturated incidence rate;    Global stability;    Lyapunov function;   

DOI  :  

来源: DOAJ

【 摘 要 】

Recently, cases of influenza virus resistance are being observed. Resistance is deadly and can cause many pandemics in future. That is why, here we investigate the situation on which the strains exist side – by – side and the difference in their mode of transmission. This paper studies two strain (resistance and non - resistance) flu model. The non-resistant strain mutates to give the resistant strain. These strains are differentiated by their incidence rates which are; bilinear and saturated for the non-resistant and saturated resistant strain respectively. This will help in studying the difference in the mode of transmission of the two strains. Equilibrium solutions are computed and Lyapunov functions are used to show their global stability. It is clear from the analysis that disease – free equilibrium is globally asymptotically stable if maxRR,RN<1. On the other hand endemic equilibrium is globally asymptotically stable if minRR,RN>1. Any strain with biggest basic reproduction ratio out performs the other. In order to support the analytic results some numerical simulations are carried out.

【 授权许可】

Unknown