38 research outputs found
The evolutionary impact of androgen levels on prostate cancer in a multi-scale mathematical model
<p>Abstract</p> <p>Background</p> <p>Androgens bind to the androgen receptor (AR) in prostate cells and are essential survival factors for healthy prostate epithelium. Most untreated prostate cancers retain some dependence upon the AR and respond, at least transiently, to androgen ablation therapy. However, the relationship between endogenous androgen levels and cancer etiology is unclear. High levels of androgens have traditionally been viewed as driving abnormal proliferation leading to cancer, but it has also been suggested that low levels of androgen could induce selective pressure for abnormal cells. We formulate a mathematical model of androgen regulated prostate growth to study the effects of abnormal androgen levels on selection for pre-malignant phenotypes in early prostate cancer development.</p> <p>Results</p> <p>We find that cell turnover rate increases with decreasing androgen levels, which may increase the rate of mutation and malignant evolution. We model the evolution of a heterogeneous prostate cell population using a continuous state-transition model. Using this model we study selection for AR expression under different androgen levels and find that low androgen environments, caused either by low serum testosterone or by reduced 5<it>α</it>-reductase activity, select more strongly for elevated AR expression than do normal environments. High androgen actually slightly reduces selective pressure for AR upregulation. Moreover, our results suggest that an aberrant androgen environment may delay progression to a malignant phenotype, but result in a more dangerous cancer should one arise.</p> <p>Conclusions</p> <p>The model represents a useful initial framework for understanding the role of androgens in prostate cancer etiology, and it suggests that low androgen levels can increase selection for phenotypes resistant to hormonal therapy that may also be more aggressive. Moreover, clinical treatment with 5<it>α</it>-reductase inhibitors such as finasteride may increase the incidence of therapy resistant cancers.</p> <p>Reviewers</p> <p>This article was reviewed by Ariosto S. Silva (nominated by Marek Kimmel) and Marek Kimmel.</p
Weather-driven malaria transmission model with gonotrophic and sporogonic cycles
Malaria is mainly a tropical disease and its transmission cycle is
heavily influenced by environment: The life-cycles of the Anopheles
mosquito vector and Plasmodium parasite are both strongly affected
by ambient temperature, while suitable aquatic habitat is necessary
for immature mosquito development. Therefore, how global warming
may affect malaria burden is an active question, and we develop
a new ordinary differential equations-based malaria transmission
model that explicitly considers the temperature-dependent Anopheles
gonotrophic and Plasmodium sporogonic cycles. Mosquito
dynamics are coupled to infection among a human population with
symptomatic and asymptomatic disease carriers, as well as temporary
immunity. We also explore the effect of incorporating diurnal
temperature variations upon transmission. Rigorous analysis of the
model show that the non-trivial disease-free equilibrium is locallyasymptotically
stable when the associated reproduction number is
less than unity (this equilibrium is globally-asymptotically for a special
case with no density-dependent larval and disease-induced host
mortality). Numerical simulations of the model, for the case where
the ambient temperature is held constant, suggest a nonlinear,
hyperbolic relationship between the reproduction number and clinical
malaria burden. Moreover, malaria burden peaks at 29.5 oC when
daily ambient temperature is held constant, but this peak decreases
with increasing daily temperature variation, to about 23–25 oC.
Malaria burden also varies nonlinearly with temperature, such that
small temperature changes influent disease mainly at marginal temperatures,
suggesting that in areas where malaria is highly endemic,
any response to global warming may be highly nonlinear and most
typically minimal, while in areas of more marginal malaria potential
(such as the East African highlands), increasing temperatures may
translate nearly linearly into increased disease potential. Finally, we observe that while explicitly modelling the stages of the Plasmodium
sporogonic cycle is essential, explicitly including the stages of
the Anopheles gonotrophic cycle is of minimal importance.National Institute for Mathematical and Biological Synthesis (NIMBioS) is an Institute sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville.http://www.tandfonline.com/loi/tjbd20am2020Mathematics and Applied Mathematic
Will vaccine-derived protective immunity curtail COVID-19 variants in the US?
Multiple effective vaccines are currently being deployed to combat the COVID-19
pandemic, and are viewed as the major factor in marked reductions of disease burden
in regions with moderate to high vaccination coverage. The effectiveness of COVID-19
vaccination programs is, however, significantly threatened by the emergence of new
SARS-COV-2 variants that, in addition to being more transmissible than the wild-type
(original) strain, may at least partially evade existing vaccines. A two-strain (one wildtype,
one variant) and two-group (vaccinated or otherwise) mechanistic mathematical
model is designed and used to assess the impact of the vaccine-induced cross-protective
efficacy on the spread the COVID-19 pandemic in the United States. Rigorous analysis of
the model shows that, in the absence of any co-circulating SARS-CoV-2 variant, the
vaccine-derived herd immunity threshold needed to eliminate the wild-type strain can be
achieved if 59% of the US population is fully-vaccinated with either the Pfizer or Moderna
vaccine. This threshold increases to 76% if the wild-type strain is co-circulating with the
Alpha variant (a SARS-CoV-2 variant that is 56% more transmissible than the wild-type
strain). If the wild-type strain is co-circulating with the Delta variant (which is estimated
to be 100% more transmissible than the wild-type strain), up to 82% of the US
population needs to be vaccinated with either of the aforementioned vaccines to achieve
the vaccine-derived herd immunity. Global sensitivity analysis of the model reveal the
following four parameters as the most influential in driving the value of the reproduction
number of the variant strain (hence, COVID-19 dynamics) in the US: (a) the infectiousness
of the co-circulating SARS-CoV-2 variant, (b) the proportion of individuals fully vaccinated
(using Pfizer or Moderna vaccine) against the wild-type strain, (c) the cross-protective
efficacy the vaccines offer against the variant strain and (d) the modification parameter
accounting for the reduced infectiousness of fully-vaccinated individuals experiencing
breakthrough infection. Specifically, numerical simulations of the model show that future
waves or surges of the COVID-19 pandemic can be prevented in the US if the two vaccines
offer moderate level of cross-protection against the variant (at least 67%). This study further suggests that a new SARS-CoV-2 variant can cause a significant disease surge in the
US if (i) the vaccine coverage against the wild-type strain is low (roughly <66%) (ii) the
variant is much more transmissible (e.g., 100% more transmissible), than the wild-type
strain, or (iii) the level of cross-protection offered by the vaccine is relatively low (e.g.,
less than 50%). A new SARS-CoV-2 variant will not cause such surge in the US if it is only
moderately more transmissible (e.g., the Alpha variant, which is 56% more transmissible)
than the wild-type strain, at least 66% of the population of the US is fully vaccinated, and the three vaccines being deployed in the US (Pfizer, Moderna, and Johnson & Johnson)
offer a moderate level of cross-protection against the variant.The Simons Foundation and the National Science Foundation.http://www.keaipublishing.com/idmam2022Mathematics and Applied Mathematic
Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus
A novel Coronavirus pandemic emerged in December of 2019, causing devastating
public health impact across the world. In the absence of a safe and effective
vaccine or antiviral, strategies for 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
these mitigation strategies. Simulations of the model, using data relevant to
COVID-19 transmission in New York state and the entire US, show that the
pandemic 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) in New
York State and the entire US decrease dramatically by 80% and 64%,
respectively, if the strict social-distancing measures implemented are
maintained until the end of May or June, 2020. This study shows that early
termination of strict social-distancing could trigger a devastating second wave
with burden similar to that projected before the onset of strict
social-distance. The use of efficacious face-masks (efficacy greater than 70%)
could lead to the elimination of the pandemic if at least 70% of the residents
of New York state use such masks 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 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 other
anti-COVID-19 intervention measures can lead to elimination of the pandemic.
The mask coverage needed to eliminate COVID-19 decreases if mask-use is
combined with strict social-distancing
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, R0, as a function of population-level bednet coverage, is derived. It is shown, owing to the phenomenon of backward bifurcation, that R0 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 R0 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.National Institute for Mathematical and Biological Synthesis (NIMBioS) is an Institute sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville. ABG also acknowledges the support, in part, of the Simons Foundation (Award #585022).http://link.springer.com/journal/2852021-05-23hj2020Mathematics and Applied Mathematic
A tumor cord model for Doxorubicin delivery and dose optimization in solid tumors
<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Methods</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusion</p> <p>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.</p
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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
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