A mathematical model for Chagas disease transmission with neighboring villages

Chagas disease has been the target of widespread control programs, primarily through residual insecticide treatments. However, in some regions like the Gran Chaco, these efforts have failed to sufficiently curb the disease. Vector reinfestation into homes and vector resistance to insecticides are possible causes of the control failure. This work proposes a mathematical model for the dynamics of Chagas disease in neighboring rural villages of the Gran Chaco region, incorporating human travel between the villages, passive vector migration, and insecticide resistance. Computational simulations across a wide variety of scenarios are presented. The simulations reveal that the effects of human travel and passive vector migration are secondary and unlikely to play a significant role in the overall dynamics, including the number of human infections. The numerical results also show that insecticide resistance causes a notable increase in infections and is an especially important source of reinfestation when spraying stops. The results suggest that control strategies related to migration and travel between the villages are unlikely to yield meaningful benefit and should instead focus on other reinfestation sources like domestic foci that survive insecticide spraying or sylvatic foci

A model for Chagas disease with oral and congenital transmission.

This work presents a new mathematical model for the domestic transmission of Chagas disease, a parasitic disease affecting humans and other mammals throughout Central and South America. The model takes into account congenital transmission in both humans and domestic mammals as well as oral transmission in domestic mammals. The model has time-dependent coefficients to account for seasonality and consists of four nonlinear differential equations, one of which has a delay, for the populations of vectors, infected vectors, infected humans, and infected mammals in the domestic setting. Computer simulations show that congenital transmission has a modest effect on infection while oral transmission in domestic mammals substantially contributes to the spread of the disease. In particular, oral transmission provides an alternative to vector biting as an infection route for the domestic mammals, who are key to the infection cycle. This may lead to high infection rates in domestic mammals even when the vectors have a low preference for biting them, and ultimately results in high infection levels in humans

Analysis of Hepatitis C Virus Decline during Treatment with the Protease Inhibitor Danoprevir Using a Multiscale Model

The current paradigm for studying hepatitis C virus (HCV) dynamics in patients utilizes a standard viral dynamic model that keeps track of uninfected (target) cells, infected cells, and virus. The model does not account for the dynamics of intracellular viral replication, which is the major target of direct-acting antiviral agents (DAAs). Here we describe and study a recently developed multiscale age-structured model that explicitly considers the potential effects of DAAs on intracellular viral RNA production, degradation, and secretion as virus into the circulation. We show that when therapy significantly blocks both intracellular viral RNA production and virus secretion, the serum viral load decline has three phases, with slopes reflecting the rate of serum viral clearance, the rate of loss of intracellular viral RNA, and the rate of loss of intracellular replication templates and infected cells, respectively. We also derive analytical approximations of the multiscale model and use one of them to analyze data from patients treated for 14 days with the HCV protease inhibitor danoprevir. Analysis suggests that danoprevir significantly blocks intracellular viral production (with mean effectiveness 99.2%), enhances intracellular viral RNA degradation about 5-fold, and moderately inhibits viral secretion (with mean effectiveness 56%). The multiscale model can be used to study viral dynamics in patients treated with other DAAs and explore their mechanisms of action in treatment of hepatitis C

The approximate and the numerical solutions of the multiscale model.

<p><b>A.</b> The short-term approximation (blue solid) is compared with the solution of the multiscale PDE model (black dashed). <b>B.</b> Difference between the long-term approximation and the solution of the multiscale PDE model. Parameter values, chosen from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002959#pcbi-1002959-t002" target="_blank">Table 2</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002959#pcbi.1002959-Rong3" target="_blank">[30]</a>, are , , , , , , , , , , , , and .</p

Populations at year 30 as functions of with .

<p>The number of infected humans, infected dogs, vectors, and infected vectors, all at year 30, as functions of . Here while all other parameters are set to the baseline values.</p

The model parameters and the baseline simulation values.

<p>The model parameters and the baseline simulation values.</p

Infected humans at year 30 as a function of and .

<p>The number of infected humans at year 30 as a function of and , where and all other parameters are set to the baseline values.</p

Parameter values with standard errors in parenthesis estimated by fitting the standard biphasic model to viral load data.

1<p>Corresponding to a half-life <i>t</i>_1/2 = 0.067 days.</p>2<p>Corresponding to a half-life <i>t</i>_1/2 = 1.65 days.</p