Understanding the implications of under-reporting, vaccine efficiency and social behavior on the post-pandemic spread using physics informed neural networks: A case study of China.

In late 2019, the emergence of COVID-19 in Wuhan, China, led to the implementation of stringent measures forming the zero-COVID policy aimed at eliminating transmission. Zero-COVID policy basically aimed at completely eliminating the transmission of COVID-19. However, the relaxation of this policy in late 2022 reportedly resulted in a rapid surge of COVID-19 cases. The aim of this work is to investigate the factors contributing to this outbreak using a new SEIR-type epidemic model with time-dependent level of immunity. Our model incorporates a time-dependent level of immunity considering vaccine doses administered and time-post-vaccination dependent vaccine efficacy. We find that vaccine efficacy plays a significant role in determining the outbreak size and maximum number of daily infected. Additionally, our model considers under-reporting in daily cases and deaths, revealing their combined effects on the outbreak magnitude. We also introduce a novel Physics Informed Neural Networks (PINNs) approach which is extremely useful in estimating critical parameters and helps in evaluating the predictive capability of our model.

Stochastic modeling, analysis, and simulation of the COVID-19 pandemic with explicit behavioral changes in Bogotá: A case study.

In this paper, a stochastic epidemiological model is presented as an extension of a compartmental SEIR model with random perturbations to analyze the dynamics of the COVID-19 pandemic in the city of Bogotá D.C., Colombia. This model incorporates the spread of COVID-19 impacted by social behaviors in the population and allows for projecting the number of infected, recovered, and deceased individuals considering the mitigation measures, namely confinement and partial relaxed restrictions. Also, the role of randomness using the concept of Brownian motion is emphasized to explain the behavior of the population. Computational experiments for the stochastic model with random perturbations were performed, and the model is validated through numerical simulations for actual data from Bogotá D.C.

Quantification of the Rupture Potential of Patient-Specific Intracranial Aneurysms under Contact Constraints.

Intracranial aneurysms (IAs) are localized enlargements of cerebral blood vessels that cause substantial rates of mortality and morbidity in humans. The rupture possibility of these aneurysms is a critical medical challenge for physicians during treatment planning. This treatment planning while assessing the rupture potential of aneurysms becomes more complicated when they are constrained by an adjacent structure such as optic nerve tissues or bones, which is not widely studied yet. In this work, we considered and studied a constitutive model to investigate the bio-mechanical response of image-based patient-specific IA data using cardiovascular structural mechanics equations. We performed biomechanical modeling and simulations of four different patient-specific aneurysms' data (three middle cerebral arteries and one internal carotid artery) to assess the rupture potential of those aneurysms under a plane contact constraint. Our results suggest that aneurysms with plane contact constraints produce less or almost similar maximum wall effective stress compared to aneurysms with no contact constraints. In our research findings, we observed that a plane contact constraint on top of an internal carotid artery might work as a protective wall due to the 16.6% reduction in maximum wall effective stress than that for the case where there is no contact on top of the aneurysm.

The Hard Lessons and Shifting Modeling Trends of COVID-19 Dynamics: Multiresolution Modeling Approach.

The COVID-19 pandemic has placed epidemiologists, modelers, and policy makers at the forefront of the global discussion of how to control the spread of coronavirus. The main challenges confronting modelling approaches include real-time projections of changes in the numbers of cases, hospitalizations, and fatalities, the consequences of public health policy, the understanding of how best to implement varied non-pharmaceutical interventions and potential vaccination strategies, now that vaccines are available for distribution. Here, we: (i) review carefully selected literature on COVID-19 modeling to identify challenges associated with developing appropriate models along with collecting the fine-tuned data, (ii) use the identified challenges to suggest prospective modeling frameworks through which adaptive interventions such as vaccine strategies and the uses of diagnostic tests can be evaluated, and (iii) provide a novel Multiresolution Modeling Framework which constructs a multi-objective optimization problem by considering relevant stakeholders' participatory perspective to carry out epidemic nowcasting and future prediction. Consolidating our understanding of model approaches to COVID-19 will assist policy makers in designing interventions that are not only maximally effective but also economically beneficial.

When Triggers Become Tigers: Taming the Autonomic Nervous System via Sensory Support System Modulation.

Personalized recovery technologies may enable individuals with Substance Use Disorder (SUD) to monitor and manage acute craving and drug use urges in ways that improve drug-seeking decisions in real-time. Direct and indirect regulation of the autonomic nervous system through sensory input monitoring and modulation may enhance control over behavioral decisions and prevent relapse. A personalized sensory support system that monitors neurophysiological reactivity and offers non-pharmacological point-in-time personalized digital interventions may increase awareness of and control over craving reactivity. It is critical to be able to detect these warning signs and intervene early and effectively. The use of wearable technologies that assess point-in-time neurophysiological escalation and shape behavioral response through personalized interventions could be transformative in allowing individuals to better manage their recovery as they transition out of institutions and move back into community settings.

Tear film dynamics with blinking and contact lens motion.

We develop a lubrication theory-based mathematical model that describes the dynamics of a tear film during blinking and contact lens (CL) wear. The model extends previous work on pre-corneal tear film dynamics during blinking by coupling the partial differential equation for tear film thickness to a dynamic model for CL motion. We explore different models for eyelid motion and also account for possible voluntary and involuntary globe (eyeball) rotation that may accompany blinking. Boundary conditions for mass flux at the eyelids are also adapted to account for the presence and motion of the CL. Our predictions for CL motion compare reasonably with existing data. Away from the eyelids the pre-lens tear film (PrLTF) is shifted, relative to its pre-corneal counterpart, in the direction of CL motion. Near the eyelids, the inflow/outflow of fluid under the eyelids also influences the PrLTF profile. We also compare our PrLTF dynamics to existing in vivo tear film thickness measurements.

Challenges and Opportunities From COVID-19 for Global Sustainable Development.

We live in unprecedented times, faced with a pandemic of monumental proportions. Not only has COVID-19 wreaked havoc across the world, it also has exposed fundamental weaknesses in healthcare systems in a number of countries. We identify challenges and opportunities that COVID-19 presents by connecting the immediate need to curb the spread of the disease to the United Nations sustainable development goals (SDGs). Considering broad social, political, and economic impacts, we focus on health disparities and the severe effects of the crisis on some populations, especially disadvantaged and underserved ones, and countries relative to others. In particular, we identify key targets for achieving SDG-3 (Good Health and Wellbeing) that will help strengthen capacities for scaling up healthcare and policy responses to understand, combat, and control COVID-19.

Connecting with Teachers through Modeling in Mathematical Biology.

In this work, we describe some effective teaching and research practices that can help to integrate mathematics and biology efficiently to enhance student learning at all levels. One of the successful approaches proposed is to employ mathematical modeling that can help transform pedagogical practices. In this regard, we introduce some modeling activities that have been shared with teachers through professional development programs and have been incorporated in the classrooms. We also present how engaging teachers in research experiences in mathematical modeling can help to transform their pedagogical practices and provide opportunities for students to consider pursuing areas at the interface of mathematics and biology.

Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions.

Over the last few decades, there have been significant developments in theoretical, experimental, and clinical approaches to understand the dynamics of cancer cells and their interactions with the immune system. These have led to the development of important methods for cancer therapy including virotherapy, immunotherapy, chemotherapy, targeted drug therapy, and many others. Along with this, there have also been some developments on analytical and computational models to help provide insights into clinical observations. This work develops a new mathematical model that combines important interactions between tumor cells and cells in the immune systems including natural killer cells, dendritic cells, and cytotoxic CD8+ T cells combined with drug delivery to these cell sites. These interactions are described via a system of ordinary differential equations that are solved numerically. A stability analysis of this model is also performed to determine conditions for tumor-free equilibrium to be stable. We also study the influence of proliferation rates and drug interventions in the dynamics of all the cells involved. Another contribution is the development of a novel parameter estimation methodology to determine optimal parameters in the model that can reproduce a given dataset. Our results seem to suggest that the model employed is a robust candidate for studying the dynamics of tumor cells and it helps to provide the dynamic interactions between the tumor cells, immune system, and drug-response systems.

Impact of Contact Constraints on the Dynamics of Idealized Intracranial Saccular Aneurysms.

The rupture potential of intracranial aneurysms is an important medical question for physicians. While most intracranial (brain) aneurysms are asymptomatic, the quantification of rupture potential of both symptomatic and asymptomatic lesions is an active area of research. Furthermore, an intracranial aneurysm constrained by an optic nerve tissue might be a scenario for a physician to deal with during the treatment process. In this work, we developed a computational model of an idealized intracranial saccular aneurysm constrained by a rigid nerve tissue to investigate the impact of constrained nerve tissues on the dynamics of aneurysms. A comparative parametric study for constraints of varying length on aneurysm surface was considered. Our computational results demonstrated the impact of contact constraints on the level of stress near the fundus and provided insight on when these constraints can be protective and when they can be destructive. The results show that lesions with long contact constraints generated higher stress (0.116 MPa), whereas lesions without constraints generated less stress (0.1 MPa) at the fundus, which indicated that lesions with nerve constraints can be protective and less likely to rupture than the lesions without constraints. Moreover, lesions with point load on the fundus generated the highest stress (18.15 MPa) and, hence, they can be destructive.

Lessons from the Ebola Outbreak: Action Items for Emerging Infectious Disease Preparedness and Response.

As the Ebola outbreak in West Africa wanes, it is time for the international scientific community to reflect on how to improve the detection of and coordinated response to future epidemics. Our interdisciplinary team identified key lessons learned from the Ebola outbreak that can be clustered into three areas: environmental conditions related to early warning systems, host characteristics related to public health, and agent issues that can be addressed through the laboratory sciences. In particular, we need to increase zoonotic surveillance activities, implement more effective ecological health interventions, expand prediction modeling, support medical and public health systems in order to improve local and international responses to epidemics, improve risk communication, better understand the role of social media in outbreak awareness and response, produce better diagnostic tools, create better therapeutic medications, and design better vaccines. This list highlights research priorities and policy actions the global community can take now to be better prepared for future emerging infectious disease outbreaks that threaten global public health and security.

Stability analysis of a model of atherosclerotic plaque growth.

Atherosclerosis, the formation of life-threatening plaques in blood vessels, is a form of cardiovascular disease. In this paper, we analyze a simplified model of plaque growth to derive physically meaningful results about the growth of plaques. In particular, the main results of this paper are two conditions, which express that the immune response increases as LDL cholesterol levels increase and that diffusion prevails over inflammation in a healthy artery.

Modelling the evaporation of a tear film over a contact lens.

A contact lens (CL) separates the tear film into a pre-lens tear film (PrLTF), the fluid layer between the CL and the outside environment, and a post-lens tear film (PoLTF), the fluid layer between the CL and the cornea. We examine a model for evaporation of a PrLTF on a modern permeable CL allowing fluid transfer between the PrLTF and the PoLTF. Evaporation depletes the PrLTF, and continued evaporation causes depletion of the PoLTF via fluid loss through the CL. Governing equations include Navier-Stokes, heat and Darcy's equations for the fluid flow and heat transfer in the PrLTF and porous layer. The PoLTF is modelled by a fixed pressure condition on the posterior surface of the CL. The original model is simplified using lubrication theory for the PrLTF and CL applied to a sagittal plane through the eye. We obtain a partial differential equation (PDE) for the PrLTF thickness that is first-order in time and fourth-order in space. This model incorporates evaporation, conjoining pressure effects in the PrLTF, capillarity and heat transfer. For a planar film, we find that this PDE can be reduced to an ordinary differential equation (ODE) that can be solved analytically or numerically. This reduced model allows for interpretation of the various system parameters and captures most of the basic physics contained in the model. Comparisons of ODE and PDE models, including estimates for the loss of fluid through the lens due to evaporation, are given.

On the stability of lung parenchymal lesions with applications to early pneumothorax diagnosis.

Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.

A sub-domain inverse finite element characterization of hyperelastic membranes including soft tissues.

Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.