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Reaction–diffusion model of infection propagation with influence of resident macrophages
1  S.M. Nikol'skii Mathematical Institute , People’s Friendship University of Russia (RUDN University), Moscow 117198, Russia
Academic Editor: Juan Torregrosa

Abstract:

In the work, we have constructed the mathematical model of respiratory viral infection propagation in the tissue with influence of resident macrophages. The model is based on reaction–diffusion equations with integral terms. In this system, the following biologically significant characteristics are determined: 1) the basic replication number, 2) the viral load, 3) the wave speed, and 4) the immunity effectiveness number. The basic replication number shows whether the infection will propagate. The viral load, i.e., the space integral from the concentration of viral particles, allows us to estimate the infectivity of the viral disease, i.e., how fast infection transmits between individuals. The wave speed corresponds to the severity of the disease. The immunity effectiveness number helps to estimate the impact of immunity in the condition of the infection propagation. The model is analyzed by applicable methods of analysis of reaction–diffusion systems and numerically. The conditions of the infection propagation, the infectivity and the severity of the disease, and the influence of the immunity are investigated, and their quantity estimates are obtained. The results may help in planning treating strategies and identification of targets for the treatment. The work was supported by the Russian Science Foundation No. 24-11-00073, https://rscf.ru/en/project/24-11-00073/. References: M. Bouzari, L. Ait Mahiout, A. Mozokhina, V. Volpert Infection propagation in a tissue with resident macrophages. Mathematical Biosciences. 2025; 381: 109399. https://doi.org/10.1016/j.mbs.2025.109399

Keywords: viral infection; inflammation; wave propagation; reaction-diffusion equations

 
 
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