Prioritizing resource allocation to reduce adverse effects of pesticide risk for endangered species

The use of pesticides promotes food security because of the multiple benefits it brings to agriculture, such as reduction in crop losses. However, the use of pesticides can be potentially harmful to non-target species. In the U.S., the Environmental Protection Agency regulates the use of pesticides to manage the risks associated with these agents and to protect species under the Endangered Species Act. As part of these regulations, pesticides must be registered and then reviewed every 15 years to ensure the use conditions are updated with the best available data. The registration and review process can invoke corrective measures to ensure protection of endangered species. However, the registration review process is highly resource and time consuming. There is currently a backlog of unreviewed pesticides, leaving a large quantity of pesticides without updated use conditions to protect species. Identifying ways to streamline this process is urgently needed. We develop a sequencing approach to address the risk assessment bottleneck in the pesticide registration and review process and identify species that would benefit most from detailed assessments. We then demonstrate the magnitude of potential efficiencies using this sequencing process for 61 terrestrial listed species in the state of California. Our results show a consistent ranking of listed species according to their relative benefits from assessment, with 90 % of the species being robustly classified across scenarios in the sensitivity analysis. We found that prioritizing the assessment of a small group of species could potentially result in high conservation benefits, and identify species in need of more detailed data for a robust sequencing. We examine how a sequencing approach can guide decisions about what species might benefit most from different levels of assessment. Our results demonstrate the conservation benefits of employing a sequencing approach to prioritize the allocation of limited resources for endangered species.

Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus

A pandemic of a novel Coronavirus emerged in December of 2019 (COVID-19), causing devastating public health impact across the world. In the absence of a safe and effective vaccine or antivirals, strategies for controlling and mitigating the burden of the pandemic are focused on non-pharmaceutical interventions, such as social-distancing, contact-tracing, quarantine, isolation, and the use of face-masks in public. We develop a new mathematical model for assessing the population-level impact of the aforementioned control and mitigation strategies. Rigorous analysis of the model shows that the disease-free equilibrium is locally-asymptotically stable if a certain epidemiological threshold, known as the reproduction number (denoted by ℛc), is less than unity. Simulations of the model, using data relevant to COVID-19 transmission dynamics in the US state of New York and the entire US, show that the pandemic burden will peak in mid and late April, respectively. The worst-case scenario projections for cumulative mortality (based on the baseline levels of anti-COVID non-pharmaceutical interventions considered in the study) decrease dramatically by 80% and 64%, respectively, if the strict social-distancing measures implemented are maintained until the end of May or June, 2020. The duration and timing of the relaxation or termination of the strict social-distancing measures are crucially-important in determining the future trajectory of the COVID-19 pandemic. This study shows that early termination of the strict social-distancing measures could trigger a devastating second wave with burden similar to those projected before the onset of the strict social-distancing measures were implemented. The use of efficacious face-masks (such as surgical masks, with estimated efficacy ≥ 70%) in public could lead to the elimination of the pandemic if at least 70% of the residents of New York state use such masks in public consistently (nationwide, a compliance of at least 80% will be required using such masks). The use of low efficacy masks, such as cloth masks (of estimated efficacy less than 30%), could also lead to significant reduction of COVID-19 burden (albeit, they are not able to lead to elimination). Combining low efficacy masks with improved levels of the other anti-COVID-19 intervention strategies can lead to the elimination of the pandemic. This study emphasizes the important role social-distancing plays in curtailing the burden of COVID-19. Increases in the adherence level of social-distancing protocols result in dramatic reduction of the burden of the pandemic, and the timely implementation of social-distancing measures in numerous states of the US may have averted a catastrophic outcome with respect to the burden of COVID-19. Using face-masks in public (including the low efficacy cloth masks) is very useful in minimizing community transmission and burden of COVID-19, provided their coverage level is high. The masks coverage needed to eliminate COVID-19 decreases if the masks-based intervention is combined with the strict social-distancing strategy.

Long-lasting insecticidal nets and the quest for malaria eradication: a mathematical modeling approach

Recent dramatic declines in global malaria burden and mortality can be largely attributed to the large-scale deployment of insecticidal-based measures, namely long-lasting insecticidal nets (LLINs) and indoor residual spraying. However, the sustainability of these gains, and the feasibility of global malaria eradication by 2040, may be affected by increasing insecticide resistance among the Anopheles malaria vector. We employ a new differential-equations based mathematical model, which incorporates the full, weather-dependent mosquito lifecycle, to assess the population-level impact of the large-scale use of LLINs, under different levels of Anopheles pyrethroid insecticide resistance, on malaria transmission dynamics and control in a community. Moreover, we describe the bednet-mosquito interaction using parameters that can be estimated from the large experimental hut trial literature under varying levels of effective pyrethroid resistance. An expression for the basic reproduction number, [Formula: see text], as a function of population-level bednet coverage, is derived. It is shown, owing to the phenomenon of backward bifurcation, that [Formula: see text] must be pushed appreciably below 1 to eliminate malaria in endemic areas, potentially complicating eradication efforts. Numerical simulations of the model suggest that, when the baseline [Formula: see text] is high (corresponding roughly to holoendemic malaria), very high bednet coverage with highly effective nets is necessary to approach conditions for malaria elimination. Further, while >50% bednet coverage is likely sufficient to strongly control or eliminate malaria from areas with a mesoendemic malaria baseline, pyrethroid resistance could undermine control and elimination efforts even in this setting. Our simulations show that pyrethroid resistance in mosquitoes appreciably reduces bednet effectiveness across parameter space. This modeling study also suggests that increasing pre-bloodmeal deterrence of mosquitoes (deterring them from entry into protected homes) actually hampers elimination efforts, as it may focus mosquito biting onto a smaller unprotected host subpopulation. Finally, we observe that temperature affects malaria potential independently of bednet coverage and pyrethroid-resistance levels, with both climate change and pyrethroid resistance posing future threats to malaria control.

Patient-specific parameter estimates of glioblastoma multiforme growth dynamics from a model with explicit birth and death rates

Glioblastoma multiforme (GBM) is an aggressive primary brain cancer with a grim prog-nosis. Its morphology is heterogeneous, but prototypically consists of an inner, largely necrotic core surrounded by an outer, contrast-enhancing rim, and often extensive tumor-associated edema beyond. This structure is usually demonstrated by magnetic resonance imaging (MRI). To help relate the three highly idealized components of GBMs (i.e., necrotic core, enhancing rim, and maximum edema ex-tent) to the underlying growth "laws," a mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. This model generates a traveling-wave solution that mimics tumor progression. We develop several novel methods to approximate key characteristics of the wave profile, which can be compared with MRI data. Several simplified forms of growth and death terms and their parameter identifiability are studied. We use several test cases of MRI data of GBM patients to yield personalized parameterizations of the model, and the biological and clinical implications are discussed.

The corona contracts in a black-hole transient

The geometry of the accretion flow around stellar-mass black holes can change on timescales of days to months^1-3. When a black hole emerges from quiescence (that is, it 'turns on' after accreting material from its companion) it has a very hard (high-energy) X-ray spectrum produced by a hot corona^4,5 positioned above its accretion disk, and then transitions to a soft (lower-energy) spectrum dominated by emission from the geometrically thin accretion disk, which extends to the innermost stable circular orbit^6,7. Much debate persists over how this transition occurs and whether it is driven largely by a reduction in the truncation radius of the disk^8,9 or by a reduction in the spatial extent of the corona^10,11. Observations of X-ray reverberation lags in supermassive black-hole systems^12,13 suggest that the corona is compact and that the disk extends nearly to the central black hole^14,15. Observations of stellar-mass black holes, however, reveal equivalent (mass-scaled) reverberation lags that are much larger¹⁶, leading to the suggestion that the accretion disk in the hard-X-ray state of stellar-mass black holes is truncated at a few hundreds of gravitational radii from the black hole^17,18. Here we report X-ray observations of the black-hole transient MAXI J1820+070^19,20. We find that the reverberation time lags between the continuum-emitting corona and the irradiated accretion disk are 6 to 20 times shorter than previously seen. The timescale of the reverberation lags shortens by an order of magnitude over a period of weeks, whereas the shape of the broadened iron K emission line remains remarkably constant. This suggests a reduction in the spatial extent of the corona, rather than a change in the inner edge of the accretion disk.

A tumor cord model for doxorubicin delivery and dose optimization in solid tumors

BACKGROUND

Doxorubicin is a common anticancer agent used in the treatment of a number of neoplasms, with the lifetime dose limited due to the potential for cardiotoxocity. This has motivated efforts to develop optimal dosage regimes that maximize anti-tumor activity while minimizing cardiac toxicity, which is correlated with peak plasma concentration. Doxorubicin is characterized by poor penetration from tumoral vessels into the tumor mass, due to the highly irregular tumor vasculature. I model the delivery of a soluble drug from the vasculature to a solid tumor using a tumor cord model and examine the penetration of doxorubicin under different dosage regimes and tumor microenvironments.

METHODS

A coupled ODE-PDE model is employed where drug is transported from the vasculature into a tumor cord domain according to the principle of solute transport. Within the tumor cord, extracellular drug diffuses and saturable pharmacokinetics govern uptake and efflux by cancer cells. Cancer cell death is also determined as a function of peak intracellular drug concentration.

RESULTS

The model predicts that transport to the tumor cord from the vasculature is dominated by diffusive transport of free drug during the initial plasma drug distribution phase. I characterize the effect of all parameters describing the tumor microenvironment on drug delivery, and large intercapillary distance is predicted to be a major barrier to drug delivery. Comparing continuous drug infusion with bolus injection shows that the optimum infusion time depends upon the drug dose, with bolus injection best for low-dose therapy but short infusions better for high doses. Simulations of multiple treatments suggest that additional treatments have similar efficacy in terms of cell mortality, but drug penetration is limited. Moreover, fractionating a single large dose into several smaller doses slightly improves anti-tumor efficacy.

CONCLUSION

Drug infusion time has a significant effect on the spatial profile of cell mortality within tumor cord systems. Therefore, extending infusion times (up to 2 hours) and fractionating large doses are two strategies that may preserve or increase anti-tumor activity and reduce cardiotoxicity by decreasing peak plasma concentration. However, even under optimal conditions, doxorubicin may have limited delivery into advanced solid tumors.

Tumor-immune interaction, surgical treatment, and cancer recurrence in a mathematical model of melanoma

Malignant melanoma is a cancer of the skin arising in the melanocytes. We present a mathematical model of melanoma invasion into healthy tissue with an immune response. We use this model as a framework with which to investigate primary tumor invasion and treatment by surgical excision. We observe that the presence of immune cells can destroy tumors, hold them to minimal expansion, or, through the production of angiogenic factors, induce tumorigenic expansion. We also find that the tumor–immune system dynamic is critically important in determining the likelihood and extent of tumor regrowth following resection. We find that small metastatic lesions distal to the primary tumor mass can be held to a minimal size via the immune interaction with the larger primary tumor. Numerical experiments further suggest that metastatic disease is optimally suppressed by immune activation when the primary tumor is moderately, rather than minimally, metastatic. Furthermore, satellite lesions can become aggressively tumorigenic upon removal of the primary tumor and its associated immune tissue. This can lead to recurrence where total cancer mass increases more quickly than in primary tumor invasion, representing a clinically more dangerous disease state. These results are in line with clinical case studies involving resection of a primary melanoma followed by recurrence in local metastases.

Melanoma is a deadly skin cancer that invades into the dermis and metastasizes into the surrounding tissue. In clinical cases, surgical excision of the primary tumor has led to widespread and accelerated growth in metastases. We develop a mathematical model describing the basic process of melanoma invasion, metastatic spread, and the anti-tumor immune response. This model is formulated using partial differential equations that describe the spatial and temporal evolution of a number of different cellular populations, and it uses a realistic skin geometry. Using simulations, we examine the importance of the immune response when a primary tumor is spawning satellite metastases. We find that local metastases can be suppressed by the immune response directed against the primary tumor, but grow aggressively following surgical treatment. We also find that moderately metastatic tumors optimally activate the local immune response against disseminated disease, and in this case tumor excision may have profound effects on metastatic growth. We conclude that surgical perturbation of the immune response controlling local metastases is one mechanism by which cancer can recur. This could have implications as to the appropriate clinical management of melanomas and other solid tumors.

The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth

Chronic HBV affects 350 million people and can lead to death through cirrhosis-induced liver failure or hepatocellular carcinoma. We analyze the dynamics of a model considering logistic hepatocyte growth and a standard incidence function governing viral infection. This model also considers an explicit time delay in virus production. With this model formulation all model parameters can be estimated from biological data; we also simulate a course of lamivudine therapy and find that the model gives good agreement with clinical data. Previous models considering constant hepatocyte growth have permitted only two dynamical possibilities: convergence to a virus free or a chronic steady state. Our model admits a third possibility of sustained oscillations. We show that when the basic reproductive number is greater than 1 there exists a biologically meaningful chronic steady state, and the stability of this steady state is dependent upon both the rate of hepatocyte regeneration and the virulence of the disease. When the chronic steady state is unstable, simulations show the existence of an attracting periodic orbit. Minimum hepatocyte populations are very small in the periodic orbit, and such a state likely represents acute liver failure. Therefore, the often sudden onset of liver failure in chronic HBV patients can be explained as a switch in stability caused by the gradual evolution of parameters representing the disease state.