https://doi.org/10.1140/epjp/s13360-022-02428-w
Regular Article
Dynamics of an infection-age HIV diffusive model with latent infected cell and Beddington–DeAngelis infection incidence
1
College of Science, Guilin University of Technology, 541004, Guilin, People’s Republic of China
2
School of Mathematics-Physics and Finance, Anhui Polytechnic University, 241000, Wuhu, People’s Republic of China
3
School of Mathematical Sciences, Jiangsu University, 212013, Zhenjiang, People’s Republic of China
4
Department of Mathematics, Sun Yat-sen University, 510275, Guangzhou, People’s Republic of China
5
Business Education, Philippine Women’s University, Ave, Malate, 1004, Metro Manila, Philippines
6
School of Data Sciences, Zhejiang University of Finance and Economics, 310018, Hangzhou, People’s Republic of China
Received:
12
November
2021
Accepted:
25
January
2022
Published online:
8
February
2022
To study the joint impact of latent infected cell, infection age, Beddington–DeAngelis incidence and viral diffusion on the HIV infection dynamics, we formulate an infection-age HIV model with the above four factors in this paper. First, the explicit expression for the basic reproduction number 
of the model is obtained, and then, we study the well-posedness of the system, which includes the existence and uniqueness of solution, the existence of global attractor. We also investigate the threshold behaviors of the steady states which are determined by . More precisely, the global stability of the uninfected equilibrium is guaranteed when 
and the infected steady state is globally asymptotically stable when 
. In addition, we show the traveling waves convergence toward two steady states as t tends to 
by constructing a suitable Lyapunov-like functional decreasing along the traveling waves. Finally, some numerical simulations are conducted to illustrate our theoretical results.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
