Optimal control of a social epidemic model with media coverage

A new social epidemic model to depict alcoholism with media coverage is proposed in this paper. Some fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated. Stability of all equilibria are studied. The existence of the optimal control pair and mathematical expressions of optimal control are obtained by Pontryagin's maximum principle. Numerical simulations are also performed to illustrate our results. Our results show that media coverage is an effective measure to quit drinking.     

Optimal control of a vectored plant disease model for a crop with continuous replanting

ABSTRACT

Vector-transmitted diseases of plants have had devastating effects on agricultural production worldwide, resulting in drastic reductions in yield for crops such as cotton, soybean, tomato, and cassava. Plant-vector-virus models with continuous replanting are investigated in terms of the effects of selection of cuttings, roguing, and insecticide use on disease prevalence in plants. Previous models are extended to include two replanting strategies: frequencyreplanting and abundance-replanting. In frequency-replanting, replanting of infected cuttings depends on the selection frequency parameter ε, whereas in abundance-replanting, replanting depends on plant abundance via a selection rate parameter also denoted as ε. The two models are analysed and new thresholds for disease elimination are defined for each model. Parameter values for cassava, whiteflies, and African cassava mosaic virus serve as a case study. A numerical sensitivity analysis illustrates how the equilibrium densities of healthy and infected plants vary with parameter values. Optimal control theory is used to investigate the effects of roguing and insecticide use with a goal of maximizing the healthy plants that are harvested. Differences in the control strategies in the two models are seen for large values of ε. Also, the combined strategy of roguing and insecticide use performs better than a single control.     

The usefulness of destructive host feeding parasitoids in classical biological control: theory and observation conflict

Abstract.

• 1 We examine the conventional wisdom among biological control practitioners that destructive host feeding is a desirable attribute in parasitoids employed for classical biological control, using both the predictions of population dynamics theory and historical data on biological control introductions of Hymenoptera against Homoptera.
• 2 Population dynamics theory predicts that destructive host feeders, compared with other parasitoids, are (a) either just as likely or more likely to become established, and (b) unable to depress host equilibria as strongly.
• 3 Analyses of the B IOC AT database suggest that among parasitoids of Homoptera destructive host feeders are superior to other parasitoids with respect to both establishment rate and success rate.
• 4 We present likely explanations for the disparity between the predictions of population dynamics theory and the results of database analysis. A partial explanation for the mismatch between theory and observation with respect to the degree of pest suppression may be that females of destructive host feeding parasitoids rely less upon hosts as a food source when alternative foods such as honeydew and nectar are plentiful.
• 5 We conclude that, despite the predictions of population dynamics theory, destructive host feeders are probably better biological control agents than other parasitoids, and certainly no worse, but that it would imprudent to use destructive host feeding as the sole, or even primary, selection criterion when seeking agents for classical biological control.

     

Coexistence in a fluctuating environment by the effect of relative nonlinearity: A minimal model

The minimal model of the “relative nonlinearity” type fluctuation-maintained coexistence is investigated. The competing populations are affected by an environmental white noise. With quadratic density dependence, the long-term growth rates of the populations are determined by the average and the variance of the (fluctuating) total density. At most two species can coexist on these two “regulating” variables; competitive exclusion would ensue in a constant environment. A numerical study of the expected time until extinction of any of the two species reveals that the criterion of mutual invasibility predicts the parameter range of long-term coexistence correctly in the limit of zero extinction threshold. However, any extinction threshold consistent with a realistic population size will allow only short-term coexistence. Therefore, our simulations question the biological relevance of mutual invasibility, as a sufficient condition of coexistence, for large density fluctuations. We calculate the average and the variance of the fluctuating density of the coexisting populations analytically via the moment-closure approximation; the results are reasonably close to the simulated behavior. Based on this treatment, robustness of coexistence is studied in the limit of infinite population size. We interpret the results of this analysis in the context of necessity of niche segregation with respect to the regulating variables using a framework theory published earlier.     

A mechanistic model for understanding invasions: using the environment as a predictor of population success

Aim We set out to develop a temperature‐ and salinity‐dependent mechanistic population model for copepods that can be used to understand the role of environmental parameters in population growth or decline. Models are an important tool for understanding the dynamics of invasive species; our model can be used to determine an organism’s niche and explore the potential for invasion of a new habitat. Location Strait of Georgia, British Columbia, Canada. Methods We developed a birth rate model to determine the environmental niche for an estuarine copepod. We conducted laboratory experiments to estimate demographic parameters over a range of temperatures and salinities for Eurytemora affinis collected from the Nanaimo Estuary, British Columbia (BC). The parameterized model was then used to explore what environmental conditions resulted in population growth vs. decline. We then re‐parameterized our model using previously published data for E. affinis collected in the Seine Estuary, France (SE), and compared the dynamics of the two populations. Results We established regions in temperature–salinity space where E. affinis populations from BC would likely grow vs. decline. In general, the population from BC exhibited positive and higher intrinsic growth rates at higher temperatures and salinities. The population from SE exhibited positive and higher growth rates with increasing temperature and decreasing salinity. These different relationships with environmental parameters resulted in predictions of complex interactions among temperature, salinity and growth rates if the two subspecies inhabited the same estuary. Main conclusions We developed a new mechanistic model that describes population dynamics in terms of temperature and salinity. This model may prove especially useful in predicting the potential for invasion by copepods transported to Pacific north‐west estuaries via ballast water, or in any system where an ecosystem is subject to invasion by a species that shares demographic characteristics with an established (sub)species.     

A model for the impact of herbicide tolerance on the performance of oilseed rape as a volunteer weed

The introduction of genetically modified, herbicide-tolerant, oilseed rape into the agricultural environment will have ramifications beyond weed control of the crop. Herbicide-tolerant rape will undoubtedly become part of established volunteer weed populations that occur in many cereal rotations, but its longevity in these populations and its impact as a weed and contaminant of future oilseed rape crops is uncertain. A life cycle model of volunteer oilseed rape was therefore constructed, incorporating existing information on physiological processes such as emergence pattern, longevity of buried seed, death rates of various structures and flowering and seeding as functions of density. The model was designed to allow interaction with control factors such as harvesting efficiency, herbicide treatment, ploughing and the sequence of crops in the rotation. Many of the physiological parameters (including seed decay rates, fecundity at high density) are uncertain, simply through lack of information in the appropriate context. Other parameters such as harvesting efficiency and herbicide kill rates, are inherently variable in farming. Accordingly, a Monte-Carlo approach, in which the model was run many times with different random realisations of parameter sets, was used to expose factors to which the seedbank was sensitive. Sets of 1250 realisations were compared for each of two extreme conditions: where herbicide could be used according to current intensive farming practice and where it was not an option (representing total herbicide tolerance). Modelled seedbank numbers after 5 yr ranged from 10^-3to 10⁴m^-2, realistic values found in arable soils. The use of herbicide, together with efficient harvesting of seed, clearly has an important suppressive effect on the oilseed rape seedbank, keeping it lower than 10²m^-2(a typical sowing rate) after 5 yr in more than 80% of realisations. In the absence of herbicide, seedbanks were invariably greater, but their absolute value depended strongly on harvesting efficiency and the extent to which high density of plants suppressed fecundity. Analysis of the time series from the simulations showed that the seedbank levels fluctuated by orders in magnitude from year to year in the absence of herbicide use. The sensitivity analysis of the life-cycle model led to the development of a simplified model for the seedbank dynamics. The model shows that the essential features of the dynamics result from an interaction between density-dependent fecundity and the perturbations due to management. Therefore predictions of the effect of herbicide tolerance on seedbank dynamics are highly uncertain without knowledge of the density dependence of fecundity. Furthermore, the sensitivity to management practices suggests that seedbank levels will be substantially more difficult to control if the efficacy of herbicide is compromised. It is concluded that the model and Monte-Carlo approach have many potential uses in exploring the effects of management, cultivar physiology and the nature of the transgenes.     

Effectiveness of zooprophylaxis in malaria control: a theoretical inquiry, with a model for mosquito populations with two bloodmeal hosts

A model for a vector mosquito population with two bloodmeal hosts (man and a domestic animal) was developed to study the influences of domestic animals on the frequency of mosquito bites on man and the endemicity of human malaria. The vector population model, including blood-feeding success in the adult stage (depending on host density and biting efficiency) and density-dependent regulation in the larval stage, was combined with the Ross-Macdonald malaria transmission model. Model analyses suggested that introduction of domestic animals easily fed upon by mosquitoes increases mosquito density and, in some situations, frequency of mosquito bites on man and the infection rate of malaria through increased success of blood-feeding. Extinction of malaria was predicted only when an extremely large number of easily accessible (as compared to man) domestic animals are introduced. Limitations in the concept of zooprophylaxis and problems of livestock management in malaria control are discussed.     

A methodology for risk analysis of plurivorous fungi in biological weed control: Sclerotinia sclerotiorum as a model

In New Zealand, research is being performed on the use of the ubiquitous plurivorous ascomycete Sclerotinia sclerotiorum, as a biocontrol agent for Cirsium arvense in pasture. As a consequence of the wide host range of this fungus, the proposed biocontrol may pose a risk to non-target arable plants. Crop disease risk is primarily due to the formation of sclerotia. These perennating bodies may directly infect susceptible crops sown at the biocontrol site in years after the biocontrol event. Additionally they may cause infection in neighbouring crops through the formation of apothecia from which airborne ascospores are dispersed. A methodology for a risk analysis is proposed, embodying both temporal and spatial processes, where the relative disease risk from biocontrol is defined as the ratio of added to naturally occurring inoculum.Exponential decay is proposed as a suitable model for the survival of sclerotia in soils beneath pastures, and data from an ongoing study are used in a preliminary parameterisation. The model is applied to published data on initial sclerotium population size and unpublished data on natural levels of soilborne sclerotia, to reveal how a withholding period, defined as the interval of time that must elapse for the ratio of added to natural inoculum to equal unity, may be calculated.For quantifying escape and aerial dispersal of ascospores from a treated pasture, three mechanistic models are proposed. Firstly, a simple one-layer model of escape, giving a provisional estimation of 81% of released ascospores escaping the pasture canopy, is discussed. Secondly, ascospore dispersal within and close to the biocontrol site (<30 m) is described by a model revealing abrupt decline in the atmospheric concentration of ascospores within short distances from the biocontrol site. Thirdly, for predicting ascospore concentrations at greater distances (>100 m), a Gaussian plume model is proposed. In a first approximation, these models are used in an example calculation to show how a hypothetical safety zone might be determined. A map of the province of Canterbury showing the locations of different agricultural activities and infestations of dense populations of C. arvense, revealed that potential biocontrol sites mostly do not border arable land and that a safety zone would therefore be feasible.The study presented here provides conceptual and mathematical frameworks for risk analysis of the use of plurivorous fungi in biological weed control, using S. sclerotiorum as an example. However, before a judgement may be made about the phytosanitory risks associated with the use of S. sclerotiorum to control C. arvense in pastures in Canterbury, the models developed in this paper must be parameterized using data collected under a wide range of conditions in the field.     

Validation of NCM460 cell model as control in antitumor strategies targeting colon adenocarcinoma metabolic reprogramming: Trichostatin A as a case study

Background

Cancer cells have extremely active metabolism, which supports high proliferation rates. Metabolic profiles of human colon cancer cells have been extensively studied, but comparison with non-tumour counterparts has been neglected.

Methods

Here we compared the metabolic flux redistribution in human colon adenocarcinoma cells (HT29) and the human colon healthy cell line NCM460 in order to identify the main pathways involved in metabolic reprogramming. Moreover, we explore if induction of differentiation in HT29 by trichostatin A (TSA) reverts the metabolic reprogramming to that of NCM460. Cells were incubated with [1,2-¹³C₂]-d-glucose as a tracer, and Mass Isotopomer Distribution Analysis was applied to characterize the changes in the metabolic flux distribution profile of the central carbon metabolism.

Results

We demonstrate that glycolytic rate and pentose phosphate synthesis are 25% lower in NCM460 with respect to HT29 cells. In contrast, Krebs cycle activity in the former was twice that recorded in the latter. Moreover, we show that TSA-induced HT29 cell differentiation reverts the metabolic phenotype to that of healthy NCM460 cells whereas TSA does not affect the metabolism of NCM460 cells.

Conclusions

We conclude that pentose phosphate pathway, glycolysis, and Krebs cycle are key players of colon adenocarcinoma cellular metabolic remodeling and that NCM460 is an appropriate model to evaluate the results of new therapeutic strategies aiming to selectively target metabolic reprogramming.

General significance

Our findings suggest that strategies to counteract robust metabolic adaptation in cancer cells might open up new avenues to design multiple hit and targeted therapies.     

基于景观生态风险格局的盐碱地分区规划防治研究——以黑龙江省林甸县为例

盐碱地分区规划防治是提高区域盐碱综合治理效果,降低治理成本的有效途径,对实现区域生态恢复、土地可持续利用和保障粮食安全具有重要实践价值。当前,在区域景观生态风险分析基础上,进行盐碱地规划防治研究的研究尚显不足。以大庆市林甸县为研究区,以景观生态学理论为视角,基于RS和GIS技术平台,综合运用最小累积阻力模型和空间分析方法,分析了生态流和生态阻力面,构建了区域景观生态风险格局;结合关键景观与盐碱地的生态廊道分析等方法,确定盐碱地防治分区;并进一步确定了防治分区中的核心防治区域。结果表明:林甸县盐碱地面积为263 km~2,其景观生态风险格局呈现西部和南部的景观生态风险等级较高,东北部、中部和西南部较低的特征,其中,高危区、重度危险区占地区总面积41.24%,集中分布在地区下游的沼泽湿地周围,说明保护沼泽湿地迫在眉睫。林甸县的两条土地盐碱化防治景观生态廊道是以最低防治成本实现土地盐碱化预防和治理的最佳区域,其主要分布在15个村(镇)上,未来应将此地区作为规划防治的核心。基于景观生态风险格局的盐碱地分区规划防治研究,为大尺度土地盐碱化综合防治提供了新的思路和方法,研究结果对林甸县未来开展土地盐碱化预防和治理提供了科学依据。     

A prospective model for the phenology of Microctonus hyperodae (Hymenoptera: Braconidae), a potential biological control agent of argentine stem weevil in New Zealand

A predictive phenological model is described for the parasitoid Microctonus hyperodae, introduced to New Zealand as a potential biological control agent against Argentine stem weevil Listronotus bonariensis. The model is based on development/temperature relationships obtained from experiments on the parasitoid in quarantine prior to its release, allowing early predictions of its phenology in different parts of the target pest's New Zealand range. In particular the model was used to predict the number of parasitoid generations each year, the degree of temporal synchrony between parasitoid adults and the susceptible adult pest stage, the order of parasitism and reproduction in the pest's life cycle as a possible basis for a simplified, discrete host/parasitoid population model, and the likely significance of ecotypic differences in development and diapause characteristics of the parasitoid. These applications demonstrate the potential for simple models to help in climate matching of classical biological control agents and estimation of their interaction with pest dynamics, using data obtainable prior to their introduction and release. In addition the model proved useful as a decision aid during the release programme, by indicating the likely effects of unusual weather and the need or otherwise for further parasitoid releases.