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Chronic hepatitis B (HBV) infection is a major cause of human suffering, and a number of mathematical models have examined the within-host dynamics of the disease. Most previous models assumed that infected hepatocytes do not proliferate; however, the effect of HBV infection on hepatocyte proliferation is controversial, with conflicting data showing both induction and inhibition of proliferation. With a family of ordinary differential equation (ODE) models, we explored the dynamical impact of proliferation among HBV-infected hepatocytes. Here, we show that infected hepatocyte proliferation in this class of models generates a threshold that divides the dynamics into two categories. Sufficiently compromised proliferation in infected cells produces complex dynamics characterized by oscillating viral loads, whereas higher proliferation generates straightforward dynamics that always results in chronic infection, sometimes with liver failure. A global stability result of the liver failure state was included as it is unique to this class of models. Finally, the model analysis motivated a testable biological hypothesis: Healthy hepatocytes are present in chronic HBV infection if and only if the proliferation of infected hepatocytes is severely impaired. 

Behavioral thermoregulation is an important defense against the negative impacts of climate change for ectotherms. In this study we examined the use of burrows by a common intertidal crab, Minuca pugnax , to control body temperature. To understand how body temperatures respond to changes in the surface temperature and explore how efficiently crabs exploit the cooling potential of burrows to thermoregulate, we measured body, surface, and burrow temperatures during low tide on Sapelo Island, GA in March, May, August, and September of 2019. We found that an increase in 1°C in the surface temperature led to a 0.70-0.71°C increase in body temperature for females and an increase in 0.75-0.77°C in body temperature for males. Body temperatures of small females were 0.3°C warmer than large females for the same surface temperature. Female crabs used burrows more efficiently for thermoregulation compared to the males. Specifically, an increase of 1°C in the cooling capacity (the difference between the burrow temperature and the surface temperature) led to an increase of 0.42-0.50°C for females and 0.34-0.35°C for males in the thermoregulation capacity (the difference between body temperature and surface temperature). The body temperature that crabs began to use burrows to thermoregulate was estimated to be around 24°C, which is far below the critical body temperatures that could lead to death. Many crabs experience body temperatures of 24°C early in the reproductive season, several months before the hottest days of the year. Because the use of burrows involves fitness trade-offs, these results suggest that warming temperatures could begin to impact crabs far earlier in the year than expected.