A Within-Host Model of Dengue Infection with a Non-Constant Monocyte Production Rate

Abstract

In this paper we modify previous models to develop a new model of within-host dengue infection without the assumption that monocyte production is constant. We show that this new model exhibits behavior not seen in previous models. We then proceed by obtaining an expression for the net reproductive rate of the virus and thus establish a stability result. We also perform a sensitivity analysis to test various treatment strategies and find that two strategies might be fruitful. One is the reduction of the infection rate of monocytes by viruses and the other, more effective, theoretical approach is to reduce the number of new viruses per infected monocyte.

A generalized within-host model of dengue infection with a non-constant monocyte production rate

“…where = αβδ + αγ δ + aδμ + αην. This gives the same result found in [27], but with a more general model. While we have not obtained a global result, our many numerical simulations of the model suggest that the disease-free equilibrium E 1 is globally asymptotically stable under the condition R 0 < 1.…”

“…In this work, we have generalized a previous model of within-host dengue infection without assuming constant monocyte production [27]. The motivation for the new approach was that observed monocyte counts can be both suppressed [13,29] and elevated [14,29] during infection.…”

“…The general desired form of the function f is shown in Figure 1. In [27], a function of the form f (S) = k 1 S exp((S * −S)/S * ) was chosen. In this case, if we choose k 1 = k 3 C * /S * , so that S * and C * are components of the disease-free equilibrium, one can verify that this function satisfies (H1)-(H5).…”