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

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

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 (R0) 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 R0=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 R0, we find that the fumigation and vector bias are the most influential parameters for determining the magnitude of R0. 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.

Modeling Public Health Campaigns for Sexually Transmitted Infections via Optimal and Feedback Control

Control of sexually transmitted infections (STIs) poses important challenges to public health authorities. Obstacles for STIs' control include low priority in public health programs and disease transmission mechanisms. This work uses a compartmental pair model to explore different public health strategies on the evolution of STIs. Optimal control and feedback control are used to model realistic strategies for reducing the prevalence of these infections. Feedback control is proposed to model the reaction of public health authorities relative to an alert level. Optimal control is used to model the optimization of available resources for implementing strategies. Numerical simulations are performed using trichomoniasis, gonorrhea, chlamydia and human papillomavirus (HPV) as study cases. HPV is non-curable, and it is analyzed only under transmission control such as condom promotion campaigns. Trichomoniasis, gonorrhea and chlamydia are curable STIs that are modeled here additionally under treatment control. Increased cost-effectiveness ratio is employed as a criterion to measure control strategies performance. The features and drawbacks of control strategies under the pair formation process are discussed.

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

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.