Modeling the effects of size-dependent harvesting strategies on the population dynamics of tropical trees.

Several forest plant species are harvested both lethally for their timber and non-lethally for their non-timber forest products by the local people for cultural and economic reasons. To maximize yield, harvesters target various life stages of these species including both adults and juveniles particularly when the number of harvestable adults decline. The demographic consequences of harvesting various plant sizes differ based on what life stage is targeted. In this paper, we develop a size-structured, seasonal system of difference equations and corresponding matrix model with time-varying harvest to model the effects of size-dependent harvesting strategies on the population dynamics of tropical trees. We illustrate numerically our work specifically on African mahogany, Khaya senegalensis, a tropical tree in Benin. Novel applications and combinations of previously established matrix compression algorithms are presented to determine certain rates in our model, with other rates coming from the use of generalized linear modeling and ordinary least squares estimation incorporating observed population data. Harvesting rates for two types of populations are estimated, one with simulated harvest and the other experiencing natural harvest. Eigenvalue analysis suggests that for the populations in our study, harvesting may not have a drastic effect on the long-term persistence of the population. However, this should be taken with caution given that our model does not account for stochastic environmental variations that can interactively reduce population growth rates.

A Data-Driven Mathematical Model of the Heroin and Fentanyl Epidemic in Tennessee.

Opioid addiction represents a major national health issue spanning decades. In recent years, prescription opioid use disorder has increasingly led to heroin and fentanyl use, with subsequent increases in mortality rates due to overdose. In this paper, we present a mechanistic, epidemic model for prescription opioid addiction and illicit heroin or fentanyl addiction which aims to better understand and predict the dynamics between these two stages of opioid use disorder. Our model aims to be both parsimonious and robust: as a system of five differential equations it is appropriate for use in theory advancement and yet it remains powerful enough to capture state-level data from Tennessee for the period 2013-2018. A key finding from our data-driven analysis is that, in the face of changing policy around prescription opioids, heroin and fentanyl are now the driving force behind the Tennessee opioid epidemic. Model projections suggest that both addictions and overdoses related to heroin and fentanyl will continue to increase in the next few years (2020-2022), even as addiction to prescription drugs continues to fall. Finally, management strategy analysis suggests that in the changing face of the epidemic, the most successful approach will target availability of treatment with subsequent monitoring of stably recovered individuals to see that they do not relapse, coincident with direct efforts to decrease opioid overdose fatalities (e.g., further availability of Naloxone).