Mathematical Model of Herpes Simplex Virus – II (HSV-II) with Global Stability Analysis
Subject Areas : International Journal of Mathematical Modelling & Computations
Eshetu Gurmu
1
,
Boka Bole
2
,
Purnachandra Koya
3
1 - Department of Mathematics, Wollega University, Nekemte, Ethiopia
2 - Department of Mathematics, Wollega University, Nekemte, Ethiopia
3 - Department of Mathematics, Wollega University, Nekemte, Ethiopia
Keywords: reproductive number, Stability Analysis, Sensitivity, HSV,
Abstract :
In this paper, a nonlinear deterministic mathematical model of ordinary differential equations has been formulated to describe the transmission dynamics of HSV-II. The well-posedness of the formulated model equations was proved and the equilibrium points of the model have been identified. In addition, the basic reproduction number that governs the disease transmission was obtained from the largest eigenvalue of the next-generation matrix. Both local and global stability of the disease-free equilibrium and endemic equilibrium point of the model equation was established using the basic reproduction number. The results show that, if the basic reproduction is less than one then the solution converges to the disease-free steady-state and the disease-free equilibrium is locally asymptotically stable. On the other hand, if the basic reproduction number is greater than one the solution converges to endemic equilibrium point and the endemic equilibrium is locally asymptotically stable. Also, sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of HSV-II. Finally, numerical simulations of the model equations are carried out using the software DE Discover 2.6.4 and MATLAB R2015b with ODE45 solver. The results of simulation show that treatment minimizes the risk of HSV-II transmission from the community and the stability of disease-free equilibrium is achievable when R0<1.