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Modelling of the immune response to viral infection
1  SM Nikolsky Mathematical Institute, People’s Friendship University of Russia (RUDN University)
Academic Editor: Antonio Di Crescenzo


The immune response includes the cascade of reactions which are aimed at destroying the pathogen and eliminating the consequences of the pathogen invasion. The understanding of the mechanism of the immune response will help to improve existing methods of treatment of infectious diseases.

Immune response includes the innate and the adaptive components. The innate immune response develops right after the pathogen invasion however it cannot always stop the infection progression. The adaptive immune response develops later during further infection progression. It acts to eliminate specific pathogens or pathogen-infected cells. The interaction of these two parts of the immune response provides the effective counteraction of the human organism to viral infection.

In this work, we construct a series of hierarchical models in order to investigate the influence of the immune response to the virus infection progression. These models are based on the local and non-local reaction-diffusion equations in one space dimension. The one-dimensional formulation allows the investigation of these models analytically, namely, evaluating the total viral load and the speed of the reaction-diffusion wave propagation. For the respiratory viral infections, the total viral load corresponds to the infectivity of the virus, i.e., the rate of infection transmission between individuals, and the wave speed corresponds to the virulence of the virus, i.e., the severity of the disease. The dependence of these characteristics on the parameters of the immune response has been investigated, and it is shown that the stronger immune response results in reduced both infectivity and virulence. The character of this dependence on the innate (interferon) and adaptive (antibodies and cytotoxic T-lymphocytes) immune response is evaluated.

Keywords: mathematical immunology; reaction-diffusion systems; immune response