Weak T-cell reactivity to hepatitis B virus (HBV) is thought to be the dominant cause for chronic HBV infection. Treatment with adefovir dipivoxil (ADV) increases the rate of HBV e antigen (HBeAg) loss; however, the immune mechanisms associated with this treatment response are not understood. Serial analysis of HBV-specific CD4+ T-cell reactivity was performed during 48 weeks of therapy with ADV and correlated with treatment outcome for 19 HBeAg-positive patients receiving ADV (n = 13) or the placebo (n = 6). We tested T-cell reactivity to HBV at seven protocol time points by proliferation, cytokine production, and enzyme-linked immunospot assays. A panel of serum cytokines was quantitated by cytokine bead array. ADV-treated patients showed increased CD4+ T-cell responses to HBV and lower serum levels of cytokines compared to those of placebo-treated patients. Enhanced CD4+ T-cell reactivity to HBV, which peaked at treatment week 16, was confined to a subgroup of ADV-treated patients who achieved greater viral suppression (5.3 +/- 0.3 log(10) copies/ml [mean +/- standard error of the mean {SEM}] serum HBV DNA reduction from baseline) and HBeAg loss, but not to ADV-treated patients with moderate (3.4 +/- 0.2 log(10) copies/ml [mean +/- SEM]) viremia reduction who remained HBeAg positive or to patients receiving the placebo. In conclusion, T-cell reactivity to HBV increases in a proportion of ADV-treated patients and is associated with greater suppression of HBV replication and HBeAg loss.
Modeling foraging via basic models is a problem that has been recently investigated from several points of view. However, understanding the effect of the spatial distribution of food on the lifetime of a forager has not been achieved yet. We explore here how the distribution of food in space affects the forager's lifetime in several different scenarios. We analyze a random forager and a smelling forager in both one and two dimensions. We first consider a general food distribution, and then analyze in detail specific distributions including constant distance between food, certain probability of existence of food at each site, and power-law distribution of distances between food. For a forager in one dimension without smell we find analytically the lifetime, and for a forager with smell we find the condition for immortality. In two dimensions we find based on analytical considerations that the lifetime ($T$) scales with the starving time ($S$) and food density ($f$) as $T\sim S^4f^{3/2}$.
We study a greedy forager who consumes food throughout a region. If the forager does not eat any food for $S$ time steps it dies. We assume that the forager moves preferentially in the direction of greatest smell of food. Each food item in a given direction contributes towards the total smell of food in that direction, however the smell of any individual food item decays with its distance from the forager. We assume a power-law decay of the smell with the distance of the food from the forager and vary the exponent $\alpha$ governing this decay. We find, both analytically and through simulations, that for a forager living in one dimension, there is a critical value of $\alpha$, namely $\alpha_c$, where for $\alpha \alpha_c$ the forager has a nonzero probability to live infinite time. We calculate analytically, the critical value, $\alpha_c$, separating these two behaviors and find that $\alpha_c$ depends on $S$ as $\alpha_c=1 + 1/\lceil S/2 \rceil$. We determine analytically that at $\alpha=\alpha_c$ the system has an essential singularity. We also study, using simulations, a forager with long-range decaying smell in two dimensions (2D) and find that for this case the forager always dies within finite time. However, in 2D we observe indications of an optimal $\alpha$ for which the forager has the longest lifetime.
We study a greedy forager who consumes food throughout a region. If the forager does not eat any food for S time steps it dies. We assume that the forager moves preferentially in the direction of greatest smell of food. Each food item in a given direction contributes towards the total smell of food in that direction, however the smell of any individual food item decays with its distance from the forager. We study both power-law decay and exponential decay of the smell with the distance of the food from the forager. For power-law decay, we vary the exponent α governing this decay, while for exponential decay we vary λ also governing the rate of the decay. For power-law decay we find, both analytically and through simulations, that for a forager living in one dimension, there is a critical value of α , namely , where for the forager will die in finite time, however for the forager has a nonzero probability to live infinite time. We calculate analytically the critical value, , separating these two behaviors and find that depends on S as . We find analytically that at the system has an essential singularity. For exponential decay we find analytically that for all λ , the forager has a finite probability to live for infinite time. We also study, using simulations, a forager with long-range decaying smell in two dimensions (2D) and find that for this case the forager always dies within finite time. However, in 2D we observe indications of an optimal α (and λ ) for which the forager has the longest lifetime.
We study a greedy forager who consumes food throughout a region. If the forager does not eat any food for $S$ time steps it dies. We assume that the forager moves preferentially in the direction of greatest smell of food. Each food item in a given direction contributes towards the total smell of food in that direction, however the smell of any individual food item decays with its distance from the forager. We assume a power-law decay of the smell with the distance of the food from the forager and vary the exponent $\alpha$ governing this decay. We find, both analytically and through simulations, that for a forager living in one dimension, there is a critical value of $\alpha$, namely $\alpha_c$, where for $\alpha<\alpha_c$ the forager will die in finite time, however for $\alpha>\alpha_c$ the forager has a nonzero probability to live infinite time. We calculate analytically, the critical value, $\alpha_c$, separating these two behaviors and find that $\alpha_c$ depends on $S$ as $\alpha_c=1 + 1/\lceil S/2 \rceil$. We determine analytically that at $\alpha=\alpha_c$ the system has an essential singularity. We also study, using simulations, a forager with long-range decaying smell in two dimensions (2D) and find that for this case the forager always dies within finite time. However, in 2D we observe indications of an optimal $\alpha$ for which the forager has the longest lifetime.
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