HPV Screening and Vaccination Strategies in an Unscreened Population: A Mathematical Modeling Study

Milwid, Rachael M.; Frascoli, Federico; Steben, Marc; Heffernan, Jane M.

doi:10.1007/s11538-018-0425-3

Cited by 6 publications

(11 citation statements)

References 40 publications

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“…One of the unique features of the brain is the composition of the extracellular matrix (ECM). While the ECM of many tissues contains large amounts of collagen and laminin, the brain’s ECM is relatively low in these fibrous ECM component, mainly found surrounding blood vessels, and more defined by the presence of large amounts of specific proteoglycans and glycoproteins [43]. It has been known for decades that the brain contains elevated levels of hyaluronic acid and heparin sulfate proteoglycans [44].…”

Section: Limits Of Current Pre-clinical Systemsmentioning

confidence: 99%

Glioblastoma’s Next Top Model: Novel Culture Systems for Brain Cancer Radiotherapy Research

Caragher

Chalmers

Gomez-Roman

2019

Cancers

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Glioblastoma (GBM), the most common and aggressive primary brain tumor in adults, remains one of the least treatable cancers. Current standard of care—combining surgical resection, radiation, and alkylating chemotherapy—results in a median survival of only 15 months. Despite decades of investment and research into the development of new therapies, most candidate anti-glioma compounds fail to translate into effective treatments in clinical trials. One key issue underlying this failure of therapies that work in pre-clinical models to generate meaningful improvement in human patients is the profound mismatch between drug discovery systems—cell cultures and mouse models—and the actual tumors they are supposed to imitate. Indeed, current strategies that evaluate the effects of novel treatments on GBM cells in vitro fail to account for a wide range of factors known to influence tumor growth. These include secreted factors, the brain’s unique extracellular matrix, circulatory structures, the presence of non-tumor brain cells, and nutrient sources available for tumor metabolism. While mouse models provide a more realistic testing ground for potential therapies, they still fail to account for the full complexity of tumor-microenvironment interactions, as well as the role of the immune system. Based on the limitations of current models, researchers have begun to develop and implement novel culture systems that better recapitulate the complex reality of brain tumors growing in situ. A rise in the use of patient derived cells, creative combinations of added growth factors and supplements, may provide a more effective proving ground for the development of novel therapies. This review will summarize and analyze these exciting developments in 3D culturing systems. Special attention will be paid to how they enhance the design and identification of compounds that increase the efficacy of radiotherapy, a bedrock of GBM treatment.

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Section: Limits Of Current Pre-clinical Systemsmentioning

confidence: 99%

Glioblastoma’s Next Top Model: Novel Culture Systems for Brain Cancer Radiotherapy Research

Caragher

Chalmers

Gomez-Roman

2019

Cancers

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“…where s ∈ R. Parameters k 2 , k 3 and 𝜆 1 ∶= 𝜆 1 (c) are defined in Lemma 3. Now, we show that (T, I, V, B) are the upper solution of system (10).…”

Section: Super-sub Solutionsmentioning

confidence: 76%

“…We see that mathematical modeling plays an important role in quantifying transmission of diseases and formulating control strategies, especially in determining the threshold of disease survival, as well as assessing disease development trends [1][2][3][4][5][6]. In particular, we also see that there has been a lot of research work on mathematical modeling, theoretical analysis, and practical applications of infectious diseases caused by viruses, such as literatures [7][8][9][10][11][12][13][14][15][16][17][18][19][20] and their references. The main research topics include the calculation of the basic reproduction number, the criteria for determining the extinction and persistence of the disease, the generation of branching phenomena and the complexity of dynamics, the fitting of model parameters, model testing and sensitivity analysis, the proposal and analysis of prevention and control measures, as well as the application of mathematical models in the epidemic of some actual viral infections, and so on.…”

Section: Introductionmentioning

confidence: 99%

Traveling waves for a diffusive virus infection model with humoral immunity, cell‐to‐cell transmission, and nonlinear incidence

Zhang

et al. 2023

Math Methods in App Sciences

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This paper is concerned with the existence and nonexistence of traveling waves of a virus infection model with humoral immunity, cell‐to‐cell transmission, and general nonlinear incidence. Our results show that the existence of traveling wave solutions is determined not only by the basic reproduction number of virus infection and the antibody response reproduction number but also by the critical wave speed . More precisely, we obtain the existence of traveling wave solution connecting infection‐free equilibrium and antibody‐free infection equilibrium for , and and connecting infection‐free equilibrium and antibody‐present infection equilibrium for , and . The existence of traveling wave solution connecting infection‐free equilibrium and antibody‐present infection equilibrium is discussed. Some numerical simulations are carried out to illustrate our analytical results.

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“…To construct the basic reproduction (1), we use the next-generation matrix approach [29]. The reader may see [30,31,32,33,34,35,36] for another example of the derivation of  0 using this method.…”

Section: The Disease-free Equilibrium and The Basic Reproduction Numbermentioning

confidence: 99%

Optimal control problem and backward bifurcation on malaria transmission with vector bias

Aldila

Angelina

2021

Heliyon

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This article aims to apply a mathematical model to investigate the spread of malaria by considering vector bias, saturated treatment, and an optimal control approach. A mathematical analysis of the equilibrium points and an investigation of the basic reproduction number show that if the basic reproduction number ( is less than one, the disease-free equilibrium is locally asymptotically stable. Furthermore, the center-manifold theory is applied to analyze the stability of the endemic equilibrium when 1 . We find that our model performs a backward bifurcation phenomenon when the saturated treatment or vector bias parameter is larger than the threshold. Interestingly, we found that uncontrolled fumigation could increase the chance of the appearance of backward bifurcation. From the sensitivity analysis of , we find that the fumigation and vector bias are the most influential parameters for determining the magnitude of . Using the Pontryagin maximum principle, the optimal control problem is constructed by treating fumigation and medical treatment parameters as the time-dependent variable. Our numerical results on the optimal control simulation suggest that time-dependent fumigation and medical treatment could suppress the spread of malaria more efficiently at minimum cost.

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HPV Screening and Vaccination Strategies in an Unscreened Population: A Mathematical Modeling Study

Cited by 6 publications

References 40 publications

Glioblastoma’s Next Top Model: Novel Culture Systems for Brain Cancer Radiotherapy Research

Glioblastoma’s Next Top Model: Novel Culture Systems for Brain Cancer Radiotherapy Research

Traveling waves for a diffusive virus infection model with humoral immunity, cell‐to‐cell transmission, and nonlinear incidence

Optimal control problem and backward bifurcation on malaria transmission with vector bias

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