Solving Allen-Cahn equations with periodic and nonperiodic boundary conditions using mimetic finite-difference operators.

In this paper, we investigate and implement a numerical method that is based on the mimetic finite difference operator in order to solve the nonlinear Allen-Cahn equation with periodic and non-periodic boundary conditions. In addition, we also analyze the performance of this mimetic-based method by using the classical heat equation with a variety of boundary conditions. We assess the performance of the mimetic-based numerical method by comparing the errors of its solutions with those obtained by a classical finite difference method and the pdepde built-in Matlab function.

Learning from the COVID-19 pandemic: A systematic review of mathematical vaccine prioritization models.

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine.

Mathematical modeling for estimating influenza vaccine efficacy: A case study of the Valencian Community, Spain.

Vaccine efficacy and its quantification is a crucial concept for the proper design of public health vaccination policies. In this work we proposed a mathematical model to estimate the efficacy of the influenza vaccine in a real-word scenario. In particular, our model is a SEIR-type epidemiological model, which distinguishes vaccinated and unvaccinated populations.

Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models.

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine.

Study of optimal vaccination strategies for early COVID-19 pandemic using an age-structured mathematical model: A case study of the USA.

In this paper we study different vaccination strategies that could have been implemented for the early COVID-19 pandemic. We use a demographic epidemiological mathematical model based on differential equations in order to investigate the efficacy of a variety of vaccination strategies under limited vaccine supply. We use the number of deaths as the metric to measure the efficacy of each of these strategies.

Mathematical Modeling of SARS-CoV-2 Omicron Wave under Vaccination Effects.

Over the course of the COVID-19 pandemic millions of deaths and hospitalizations have been reported. Different SARS-CoV-2 variants of concern have been recognized during this pandemic and some of these variants of concern have caused uncertainty and changes in the dynamics. The Omicron variant has caused a large amount of infected cases in the US and worldwide.

Dynamics of toxoplasmosis in the cat's population with an exposed stage and a time delay.

We propose a new mathematical model to investigate the effect of the introduction of an exposed stage for the cats who become infected with the T. gondii parasite, but that are not still able to produce oocysts in the environment. The model considers a time delay in order to represent the duration of the exposed stage.

Mathematical modeling to study the impact of immigration on the dynamics of the COVID-19 pandemic: A case study for Venezuela.

We propose two different mathematical models to study the effect of immigration on the COVID-19 pandemic. The first model does not consider immigration, whereas the second one does. Both mathematical models consider five different subpopulations: susceptible, exposed, infected, asymptomatic carriers, and recovered.

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach.

The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020. Currently, there are only a few approved vaccines, each with different efficacies and mechanisms of action. Moreover, vaccination programs in different regions may vary due to differences in implementation, for instance, simply the availability of the vaccine.

Analysis of Delayed Vaccination Regimens: A Mathematical Modeling Approach.

The first round of vaccination against coronavirus disease 2019 (COVID-19) began in early December of 2020 in a few countries. There are several vaccines, and each has a different efficacy and mechanism of action. Several countries, for example, the United Kingdom and the USA, have been able to develop consistent vaccination programs where a great percentage of the population has been vaccinated (May 2021).

Impact of Infective Immigrants on COVID-19 Dynamics.

The COVID-19 epidemic is an unprecedented and major social and economic challenge worldwide due to the various restrictions. Inflow of infective immigrants have not been given prominence in several mathematical and epidemiological models. To investigate the impact of imported infection on the number of deaths, cumulative infected and cumulative asymptomatic, we formulate a mathematical model with infective immigrants and considering vaccination.

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility.

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models.

Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness.

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population.

The rate of viral transfer between upper and lower respiratory tracts determines RSV illness duration.

Respiratory syncytial virus can lead to serious lower respiratory infection (LRI), particularly in children and the elderly. LRI can cause longer infections, lingering respiratory problems, and higher incidence of hospitalization. In this paper, we use a simplified ordinary differential equation model of viral dynamics to study the role of transport mechanisms in the occurrence of LRI.

Effect of stochasticity on coinfection dynamics of respiratory viruses.

Background: Respiratory viral infections are a leading cause of mortality worldwide. As many as 40% of patients hospitalized with influenza-like illness are reported to be infected with more than one type of virus. However, it is not clear whether these infections are more severe than single viral infections.

Superinfection and cell regeneration can lead to chronic viral coinfections.

Molecular diagnostic techniques have revealed that approximately 43% of the patients hospitalized with influenza-like illness are infected by more than one viral pathogen, sometimes leading to long-lasting infections. It is not clear how the heterologous viruses interact within the respiratory tract of the infected host to lengthen the duration of what are usually short, self-limiting infections. We develop a mathematical model which allows for single cells to be infected simultaneously with two different respiratory viruses (superinfection) to investigate the possibility of chronic coinfections.

A quantitative assessment of dynamical differences of RSV infections in vitro and in vivo.

Experimental results in vitro and in animal models are used to guide researchers in testing vaccines or treatment in humans. However, viral kinetics are different in vitro, in animals, and in humans, so it is sometimes difficult to translate results from one system to another. In this study, we use a mathematical model to fit experimental data from multiple cycle respiratory syncytial virus (RSV) infections in vitro, in african green monkey (AGM), and in humans in order to quantitatively compare viral kinetics in the different systems.

Modeling of fusion inhibitor treatment of RSV in African green monkeys.

Respiratory syncytial virus (RSV) is a respiratory infection that can cause serious illness, particularly in infants. In this study, we test four different model implementations for the effect of a fusion inhibitor, including one model that combines different drug effects, by fitting the models to data from a study of TMC353121 in African green monkeys. We use mathematical modeling to estimate the drug efficacy parameters, ε, the maximum efficacy of the drug, and EC, the drug concentration needed to achieve half the maximum effect.

A comparison of RSV and influenza in vitro kinetic parameters reveals differences in infecting time.

Influenza and respiratory syncytial virus (RSV) cause acute infections of the respiratory tract. Since the viruses both cause illnesses with similar symptoms, researchers often try to apply knowledge gleaned from study of one virus to the other virus. This can be an effective and efficient strategy for understanding viral dynamics or developing treatment strategies, but only if we have a full understanding of the similarities and differences between the two viruses.

Quantifying rotavirus kinetics in the REH tumor cell line using in vitro data.

Globally, rotavirus is the most common cause of diarrhea in children younger than 5 years of age, however, a quantitative understanding of the infection dynamics is still lacking. In this paper, we present the first study to extract viral kinetic parameters for in vitro rotavirus infections in the REH cell tumor line. We use a mathematical model of viral kinetics to extract parameter values by fitting the model to data from rotavirus infection of REH cells.

Prediction of the respiratory syncitial virus epidemic using climate variables in Bogotá, D.C.

lntroduction: The respiratory syncitial virus is one of the most common causes of mortality in children and older adults in the world. Objective: To predict the initial week of outbreaks and to establish the most relevant climate variables using naive Bayes classifiers and receiver operating characteristic curves (ROC). Materials and methods: The initial dates of the outbreaks in children less than five years old for the period 2005-2010 were obtained for Bogotá, Colombia.

Modeling Chagas Disease at Population Level to Explain Venezuela's Real Data.

Objectives: In this paper we present an age-structured epidemiological model for Chagas disease. This model includes the interactions between human and vector populations that transmit Chagas disease.

Methods: The human population is divided into age groups since the proportion of infected individuals in this population changes with age as shown by real prevalence data.

A comparison of methods for extracting influenza viral titer characteristics.

Viral titer data collected in vitro or in vivo is often analyzed by extracting viral titer characteristics such as peak viral titer, time of viral peak and area under the curve (AUC). Researchers compare these characteristics in the absence and presence of various concentrations of antivirals in an attempt to quantify the effect of antivirals. Often these characteristics are estimated using only measured data points, although fitting of simple mathematical models to estimate these parameters is becoming more prevalent.

Assessing Uncertainty in A2 Respiratory Syncytial Virus Viral Dynamics.

Respiratory syncytial virus (RSV) is the most common cause of bronchiolitis and pneumonia in children younger than 1 year of age in the United States. Moreover, RSV is being recognized more often as a significant cause of respiratory illness in older adults. Although RSV has been studied both clinically and in vitro, a quantitative understanding of the infection dynamics is still lacking.