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<p>The main purpose of this work is to investigate the existence and nonexistence of traveling waves for a virus infection model with adaptive immunity, virus-to-cell infection and cell-to-cell transmission. The virus-to-cell and cell-to-cell incidence rates are modeled by general nonlinear functions. The basic reproduction numbers are calculated for virus infection, antibody immune response, cytotoxic T lymphocytes (CTL) immune response, CTL immune competition, and antibody immune competition. By introducing an auxiliary nonlinear differential system and applying the Schauder’s fixed point theorem, combined with the method of upper-lower solutions, we prove the existence of traveling waves dependent not only on the five reproduction numbers but also on the critical wave speed. Moreover, we show that these traveling waves connect the infection-free equilibrium to each of the other four equilibria, namely the immune-free infection equilibrium, the infection equilibrium with only antibody immune defense, the infection equilibrium with only CTL immune response and the CTL-antibody-present infection equilibrium. Finally, an application is provided and some numerical simulations are performed to illustrate the theoretical results obtained.</p>

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Traveling waves for a general diffusive virus infection model with both virus-to-cell and cell-to-cell transmissions and adaptive immunity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月15日

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  • Séverin Foko,
  • Chuene Thama Duba,
  • Calvin Tadmon,
  • Jean M. -S. Lubuma

摘要

The main purpose of this work is to investigate the existence and nonexistence of traveling waves for a virus infection model with adaptive immunity, virus-to-cell infection and cell-to-cell transmission. The virus-to-cell and cell-to-cell incidence rates are modeled by general nonlinear functions. The basic reproduction numbers are calculated for virus infection, antibody immune response, cytotoxic T lymphocytes (CTL) immune response, CTL immune competition, and antibody immune competition. By introducing an auxiliary nonlinear differential system and applying the Schauder’s fixed point theorem, combined with the method of upper-lower solutions, we prove the existence of traveling waves dependent not only on the five reproduction numbers but also on the critical wave speed. Moreover, we show that these traveling waves connect the infection-free equilibrium to each of the other four equilibria, namely the immune-free infection equilibrium, the infection equilibrium with only antibody immune defense, the infection equilibrium with only CTL immune response and the CTL-antibody-present infection equilibrium. Finally, an application is provided and some numerical simulations are performed to illustrate the theoretical results obtained.