• S. V. Baranovsky National University of Water and Environmental Engineering, Rivne, Ukraine
  • A. Ya. Bomba National University of Water and Environmental Engineering, Rivne, Ukraine
Keywords: infectious disease model, biinfection model, dynamic systems with delay, asymptotic methods, singularly perturbed problems, concentrated influences, logistics dynamics


A model of viral biinfection has been modified to predict the development of the disease process, taking into account diffusion perturbations, concentrated influences, as well as the logistic dynamics of antigen and antibody populations. The solution of the original model singularly perturbed problem with a delay is presented in the form of numerically asymptotic approximations of solutions to the corresponding sequence of problems without delay. The results of computer experiments are presented, which demonstrate a decrease in the rate of model growth of the antigenic population, taking into account the diffusion «scattering» of the active factors of the process. Also illustrated is the exacerbation of the nature of the course of a previously stabilized chronic disease due to the redistribution of the resources of the immune system to overcome infection with another viral infection. It was noted that such exacerbation significantly increases under conditions of low model levels of logistical limitation of the volume of antibody synthesis. It is emphasized that an excessive increase in the model concentration of chronic disease antigens due to a too low level of logistical limitation of the antibody population leads to a significant predictive damage to the target organ and a corresponding decrease in the overall power of the immune response. Taking into account such an effect is important when predicting the development of the disease in practical decision-making situations regarding the formation of the most effective treatment programs, including the use of various concentrated effects of immunotherapy.


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