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Complex Dynamics for an Immunosuppressive Infection Model with Virus Stimulation Delay and Nonlinear Immune Expansion

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Abstract

This work brings nonlinear Beddington–DeAngelis immune expansion and virus stimulation delay into a classical immunosuppressive infection model developed by Komarova et al. (Proc Natl Acad Sci USA 100(4):1855–1860, 2003) to seek for the effective strategies in realizing the “functional cure” goal with sustained immunity. Compared with the classical model, stability analysis indicates that the nonlinear immune expansion brings about qualitative changes in dynamic features, and new immune control equilibrium appears even under the weak viral inhibitory effects. Global stability analysis for the model without delay shows that the unique local stable equilibrium is also globally asymptotically stable, and it just exhibits bistability dynamics and saddle-node bifurcation. While the virus stimulation delay induces plenty of complex dynamical features, including Hopf bifurcation, homoclinic, heteroclinic and singular closed orbits, sustained and transient oscillations. Numerical investigation reveals that a reduction in the two key parameters involved in the nonlinear immune expansion (i.e., immune competition intensity and virus inhibition intensity) can lengthen the bistable interval and expand the virus-control region, which enables the model to more readily stabilize at either an immune control equilibrium or a periodic orbit, achieving sustained immunity. Moreover, several strategies including the drug therapies targeted at the reduction in the two key parameters and the delay, could effectively shorten therapy duration, as well as the implementation of the weak intensity of therapy still can realize sustained immunity if the delay remains relatively small.

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Acknowledgements

This work is supported partially by National Natural Science Foundation of China (Nos. 12001178, 12271147) and Innovative Training Program for College Students of Hubei Minzu University (No. S202010517021).

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  1. School of Mathematics and Statistics, Hubei Minzu University, Enshi, 445000, People’s Republic of China

    Yi Chen, Lianwen Wang, Zhijun Liu & Yating Wang

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  1. Yi Chen
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Chen, Y., Wang, L., Liu, Z. et al. Complex Dynamics for an Immunosuppressive Infection Model with Virus Stimulation Delay and Nonlinear Immune Expansion. Qual. Theory Dyn. Syst. 22, 118 (2023). https://doi.org/10.1007/s12346-023-00814-y

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