Abstract
A viral infection model with a nonlinear infection rate is constructed based on empirical evidences. Qualitative analysis shows that there is a degenerate singular infection equilibrium. Furthermore, bifurcation of cusp-type with codimension two (i.e., Bogdanov-Takens bifurcation) is confirmed under appropriate conditions. As a result, the rich dynamical behaviors indicate that the model can display an Allee effect and fluctuation effect, which are important for making strategies for controlling the invasion of virus.
Highlights
Mathematical models can provide insights into the dynamics of viral load in vivo
As Regoes et al 11, we take the nonlinear infection rate into account by relaxing the mass-action assumption that is made in 1.2 and obtain dx dt λ − dx − β y x, 1.3 dy dt β y x − ay, where the infection rate per susceptible cell, β y, is a sigmoidal function of the virus parasite concentration because the number of infected cells y t can be considered as a measure of virus load e.g., see 5–7, which is represented in the following form: βy y/ID50 κ y/ID50 κ
The main purpose of this paper is to study the effect of the nonlinear infection rate on the dynamics of 1.6
Summary
A viral infection model with a nonlinear infection rate is constructed based on empirical evidences.
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