A Within-Host Model of Dengue Infection with a Non-Constant Monocyte Production Rate

In this paper we modify previous models to develop a new model of within-host dengue infection without the assumption that monocyte production is constant. We show that this new model exhibits behavior not seen in previous models. We then proceed by obtaining an expression for the net reproductive rate of the virus and thus establish a stability result. We also perform a sensitivity analysis to test various treatment strategies and find that two strategies might be fruitful. One is the reduction of the infection rate of monocytes by viruses and the other, more effective, theoretical approach is to reduce the number of new viruses per infected monocyte.

A growing captive population erodes the wild Red-crowned Cranes(Grus japonensis) in China

Background: The Red-crowned Crane(Grus japonensis) is an endangered bird species and while the wild population continues to decrease in China, the captive population has dramatically increased over the last two decades. We hypothesized that some of the captive Red-crowned Cranes originated from the wild and that a growing captive population is eroding the wild population in China.Methods: We surveyed the size of the population and determined the average annual growth rate, reproductive success rate and mortality rate of captive Red-crowned Cranes in 2013 in China. We assessed this erosion effect through mathematical models, in which the size of the captive Red-crowned Crane population was determined from the annual growth rate, the reproductive success rate and the rate of mortality.Results: We found there were a total of 1520 captive Red-crowned Cranes in 2013 in China, with an average annual gro-wth rate of 7.46%, a reproductive success rate of 9.17% and a mortality rate of 3.6%. We found that approximately 1027 supplementary Red-crowned Cranes per year and a total of 244, over the 14 year period from 1999 to 2013, were needed to account for the growing captive population in China.Conclusion: We conclude that the 244 birds probably came from the wild by taking eggs and capturing juveniles or adults and hence accepted the hypothesis. Perhaps more surprisingly, our annual estimate of the number of supplementary Red-crowned Cranes in captive populations is very conservative, with the erosion effect substantially underestimated, because the total number of captive Red-crowned Cranes in 2013 was underestimated, with the annual reproductive success rate in zoos overestimated. The existence of an erosion effect provides a new perspective for the interpretation of why the Red-crowned Crane population in the wild continues to decrease. In our opinion, it is important to understand the consequences of this erosion effect on the management and conservation of this endangered bird species in China.

Modeling and Optimization of Interaction between Small Coastal Pelagic Fish, their Biological Predators and Fishermen

Small coastal pelagic fish are one of the fish families most affected by sea fishing. This man-made phenomenon leads to an imbalance in the marine and coastal ecosystem and is one of the main causes of migration north and offshore of the ranges. We used the ordinary differential equations to model the interactions existing between small pelagic resources and fishermen. Modelling follows the same of the Lotka-Volterra equations with a difference in the number of variables. This study confirmed the instability of the marine ecosystem. The objective is first of all to model a system of three interacting individuals composed of two distinct types of predators and two types of prey, and then optimise this interaction with the aim of conserving biodiversity in the ecosystem under study. Determining the Jacobian matrix made it possible to calculate the reproduction rate basic (R0). The study of the strong connectedness has made it possible to reduce the number of variables without losing the objective of the study. A computer program implemented on the language computer python facilitated the visualisation of the results.

Global Dynamics of a New Huanglongbing Transmission Model with Quarantine Measures

Incorporating plant-dependent saturated reproduction function, chemical insecticide, and its resistance, a plant-vector-virus model which describes the spread of infection throughout the plant by the insect is investigated in this paper. First of all, the basic reproduction number R0 is obtained by using the method of the next generation matrix, and the existence of disease-free equilibrium and endemic equilibrium is examined. Then we show that the disease-free steady state is globally asymptotically stable if R0 1, the system is uniformly persistent and the endemic equilibrium is local stability. Finally, numerical simulation is carried out to illustrate our theoretical results. Our result implies that insecticide resistance has a vital impact on the control of plant diseases.

Effect of age on reproductive attributes of an aphidophagous ladybird, Cheilomenes sexmaculata

The effect of both male and female age was investigated on certain reproductive attributes, viz. mating incidence, mating duration, fecundity, percent egg viability, ratio of reproductive and non-reproductive periods and reproductive rate, of an aphidophagous ladybird, Cheilomenes sexmaculata （Fabricius）. Females started mating at the age of 8 hours post-emergence （PE） and males at the age of 2 days PE. Mating in the laboratory was a maledominated phenomenon. The mating duration and reproductive rate of 10-day-old females when mated with males of varying ages increased up to the male age of 60 days, and thereafter decreased, whereas, fecundity, egg viability and ratio of reproductive and non-reproductive periods increased up to the male age of 50 days, and thereafter declined. However, when females of varying ages were mated with 10-day-old males, fecundity and reproductive rate increased up to 40 days of female age, respectively, then decreased. The ratio of reproductive and non-reproductive periods increased with increasing age of females. Mating age for optimal reproductive output was 10-50-day-old males and NE to 40-day-old females. Reproductive cessation in males was recorded after 50 days PE, whereas in females at the age of 40 days PE. Higher mating durations lead to elevated reproductive rates. Delay in the reproductive phase was positively correlated with longevity. The results of this study may aid mass multiplication of this ladybird by identifying and promoting usage of adults of optimal age, Our results also enhance our understanding of the effect of age on reproductive attributes in ladybirds.