Abstract
In this paper, a pathogen dynamics model with capsids and saturated incidence has been proposed and analyzed. Cytotoxic T Lymphocyte (CTL) immune response and two distributed time delays have been incorporated into the model. The nonnegativity and boundedness of the solutions of the proposed model have been shown. Two threshold parameters which fully determine the existence and stability of the three steady states of the model have been computed. Using the method of Lyapunov function, the global stability of the steady states of the model has been established. The theoretical results have been confirmed by numerical simulations.
Highlights
Cytotoxic T Lymphocyte (CTL) immune response has been incorporated into mathematical models of different viral pathogen infections
Model (5)–(9) assumes a bilinear form for the pathogen-susceptible incidence rate which are based on the mass action principle. Such bilinear form is imperfect to depict the dynamical behavior of the viral pathogen infection in detail
We compute R0 = 0.4411 and R1 = 0.3115, which means that the system has an pathogen-free steady state D0 and it is globally asymptotically stable (GAS) based on Lemma 2 and Theorem 1
Summary
The mathematical models have been introducing to describe human viral pathogens dynamics such as HIV,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] HBV,[22,23] HCV,[24,25] and HTLV-I.26,27 The basic pathogen dynamics model contains three compartments: susceptible cells (s), infected cells (i) and pathogens (p).[2]. The basic pathogen dynamics model contains three compartments: susceptible cells (s), infected cells (i) and pathogens (p).[2] The model has been improved to take the immune response into account. CTL immune response has been incorporated into mathematical models of different viral pathogen infections The generation and death rate constants of capsids. Model (5)–(9) assumes a bilinear form for the pathogen-susceptible incidence rate which are based on the mass action principle Such bilinear form is imperfect to depict the dynamical behavior of the viral pathogen infection in detail This paper is aimed to study the qualitative behavior of a pathogen dynamics model with capsids and CTL immune response where the pathogensusceptible incidence is given by a saturated form γs(t)p(t) 1+αp(t).
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