HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided.

To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases.

Estimating individual tree diameters at breast height (DBH) from delineated crowns and tree heights on the basis of airborne light detection and ranging (LiDAR) data provides a good opportunity for large-scale forest inventory. Generally, ground-based measurements are more accurate, but LiDAR data and derived DBH values can be obtained over larger areas for a relatively smaller cost if a right procedure is developed. A nonlinear least squares (NLS) regression is not an appropriate approach to predict the aboveground biomass (AGB) of individual trees from the estimated DBH because both the response variable and the regressor are subject to measurement errors. In this study, a system of compatible individual tree DBH and AGB error-in-variable models was developed using error-in-variable regression techniques based on both airborne LiDAR and field-measured datasets of individual Picea crassifolia Kom. trees, collected in northwestern China. Two parameter estimation algorithms, i.e., the two-stage error-in-variable model (TSEM) and the nonlinear seemingly unrelated regression (NSUR), were proposed for estimating the parameters in the developed system of compatible individual tree DBH and AGB error-in-variable models. Moreover, two model structures were applied to estimate AGB for comparison purposes: NLS with AGB estimation depending on DBH (NLS&DD) and NLS with AGB estimation not depending on DBH (NLS&NDD). The results showed that both TSEM and NSUR led to almost the same parameter estimates for the developed system. Moreover, the developed system effectively accounted for the inherent correlation between DBH and AGB as well as for the effects of measurement errors in the DBH on the predictions of AGB, whereas NLS&DD and NLS&NDD did not. A leave-one-out cross-validation indicated that the prediction accuracy of the developed system of compatible individual tree DBH and AGB error-in-variable models with NSUR was the highest among those estimated by the four methods evaluated, but, statistically, the accuracy improvement was not significantly different from zero. The main reason might be that, except for the measurement errors, other source errors were ignored in the modeling. This study implies that, overall, the proposed method provides the potential to expand the estimations of both DBH and AGB from individual trees to stands by combining the error-in-variable modeling and LiDAR data and improve their estimation accuracies, but its application needs to be further validated by conducting a systematical uncertainty analysis of various source errors in a future study.