Homoclinic and heteroclinic solutions to a hepatitis C evolution model

Tadas Telksnys 1 , Zenonas Navickas 1 , Romas Marcinkevicius 2 , Maosen Cao 3 ,  and Minvydas Ragulskis 1
• 1 Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas, Lithuania
• 2 Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas, Lithuania
• 3 Department of Engineering Mechanics, Hohai University, 210098, Nanjing, China

Abstract

Homoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper. Inverse balancing and generalized differential techniques enable derivation of necessary and sufficient existence conditions for homoclinic/heteroclinic solutions in the considered system. It is shown that homoclinic/heteroclinic solutions do appear when the considered system describes biologically significant evolution. Furthermore, it is demonstrated that the hepatitis C virus evolution model is structurally stable in the topological sense and does maintain homoclinic/heteroclinic solutions as diffusive coupling coefficients tend to zero. Computational experiments are used to illustrate the dynamics of such solutions in the hepatitis C evolution model.

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