Stochastic modeling has become an essential tool for studying biochemical reaction networks. There is a growing need for user-friendly and feature-complete software for model design and simulation. To address this need, we present GillesPy2, an open-source framework for building and simulating mathematical and biochemical models. GillesPy2, a major upgrade from the original GillesPy package, is now a stand-alone Python 3 package. GillesPy2 offers an intuitive interface for robust and reproducible model creation, facilitating rapid and iterative development. In addition to expediting the model creation process, GillesPy2 offers efficient algorithms to simulate stochastic, deterministic, and hybrid stochastic-deterministic models.

According to the Target Theory, the tumor population is divided into multiple different subpopulations, called targets, based on the diverse effects of ionizing radiation on human cells. Radiation particles can cause single or double-strand break(s). As such, cells are divided into three subpopulations, namely cells with no DNA fragmentation, cells with DNA single-strand breaks, and cells with DNA double-strand breaks. This work introduces a hybrid differential equation model, with coefficients described by random variables representing transition rates between targets. The model is utilized to simulate the dynamics of targets and describes the cell damage heterogeneity and the repair mechanism between two consecutive dose fractions. Therefore, a new definition of tumor lifespan based on population size is achieved. Stability and bifurcation analysis are performed. Finally, the probability of target inactivity after radiation and the probability of target re-activation following the repair mechanism are evaluated with respect to the tumor lifespan.

Increasing temperatures have raised concerns over the potential effect on disease spread. Temperature is a well known factor affecting mosquito population dynamics and the development rate of the malaria parasite within the mosquito, and consequently, malaria transmission. A sinusoidal wave is commonly used to incorporate temperature effects in malaria models, however, we introduce a seasonal malaria framework that links data on temperature-dependent mosquito and parasite demographic traits to average monthly regional temperature data, without forcing a sinusoidal fit to the data. We introduce a spline methodology that maps temperature-dependent mosquito traits to time-varying model parameters. The resulting non-autonomous system of differential equations is used to study the impact of seasonality on malaria transmission dynamics and burden in a high and low malaria transmission region in Malawi. We present numerical simulations illustrating how temperature shifts alter the entomological inoculation rate and the number of malaria infections in these regions.

In this study, we used a simple epidemic model and 2015–16 outbreak data of Chikungunya, Dengue and Zika viruses, arthropod mediated infections that are transmitted by the common mosquito vector Aedes aegypti, from Mexico to quantify the transmission rates (humans-to-mosquitoes and mosquitoes-to-humans) of the three diseases. The transmission rates are estimated for the observed data and consequently the basic reproduction number (R0) is calculated 6.740, 2.904 and 12.6283 for Chikungunya, Dengue and Zika infection, respectively. Using the estimated parameters for the three diseases, we evaluated self-imposed controls measures by the population as a result of fear-driven behavior changes often seen during an outbreak. Furthermore, the sensitivity analysis reveals that the parameter 'mosquitoes death rate' is the most sensitive one for R0. Simulations of controlled basic reproduction number are also performed for all considered control measures. This study is likely to enrich the understanding about transmission of such viral infections and control strategies.

Liver cirrhosis and hepatocellular carcinoma disease caused by the Hepatitis C virus (HCV) infection. Inside this article, a deterministic model has been formulated and analyzed for the transmission of HCV in the liver cells. We have also considered two types of viral strain (wild and mutant).  We have also projected a mathematical model of the effect of Sofosbuvir  (SOF) together with Velpatasvir (VEL) antiviral therapy in HCV infected patients. Our analytical and numerical findings reveal that the optimal schedule of treatment for the best result should be obtained by choosing the best strategy depending on the circumstances.

In this work, we present an approach called Disease Informed Neural Networks (DINNs) that can be employed to effectively predict the spread of infectious diseases. We build on the application of physics informed neural network (PINNs) to SIR compartmental models and expand it to a scaffolded family of mathematical models describing various infectious diseases. We show how the neural networks are capable of learning how diseases spread, forecasting their progression, and finding their unique parameters (e.g., death rate). To demonstrate the robustness and efficacy of DINNs, we apply the approach to eleven highly infectious diseases that have been modeled in increasing levels of complexity. Our computational experiments suggest that DINNs is a reliable candidate to effectively learn the dynamics of their spread and forecast their progression into the future from available real-world data. Code and data can be found here: https://github.com/Shaier/DINN

It is known that in oxygen concentration profiles for capillary beds of skeletal muscles, radial diffusion most likely has considerably more effect on oxygen transport in long and parallel capillary beds than axial diffusion. However, axial diffusion may still play a significant role in oxygen transport in tissue, especially in relatively short pathways. Our model adds to known solutions the component of axial diffusion to multi-capillary beds inside a tissue cylinder, where arbitrary characteristics include random locations and uneven oxygen strengths. Discussion of the solutions for oxygen supply in multicapillary beds near the arterial ends, in the central regions, and near the venous ends in capillaries is introduced in the remainder of the article. Our prime model builds on known solutions involving circular regions by adding a $Z$-axis and by accounting for circular cylindrical tissue around multiple capillaries. To account for relatively small longitudinal diffusivities, we use perturbation methods to solve the associated governing equations.

Contact tracing can be an effective measure to control emerging infectious diseases, but the efficacy of contact tracing measures can depend upon the willingness of individuals to get be tested even when they are symptomatic. In this paper, we examine the effects of symptomatic individuals getting tested and the use of contact tracing in a network model of disease transmission. We utilize a network model to resolve the influence of contact patterns between individuals as apposed to assuming mass action where all individuals are connected to each other.  We find that the effects of self-reporting and contact tracing vary depending on the structure of the network. We also compare the results from the network model with an analogous ODE model that assumes mass action and demonstrate how the results can be dramatically different.

In this paper we use a data driven SIR model to capture the dynamics of the spread of the SARS-CoV-2 pandemic in the state of Michigan. The model is then used to formulate an optimal control problem in which we perform sensitivity analysis involving vaccine efficacy and capacity, and vaccination willingness by the public. We obtain numerical approximations for best strategies for vaccination, treatment, and social distancing measures and their effect on the spread of the virus.

Evolutionary game theory (EGT) analyzes the stability of competing strategies for withstanding selective pressures within a population over generations. Under rapid shifts in selective pressures (e.g., introduction of a novel pathogen), evolutionary rescue may preserve a population, but how it may re-stabilize over generations is also critical for estimations of population persistence. Here, we present a simple model that couples EGT with epidemiology to investigate evolutionary rescue under a novel and epidemiologically-driven dynamic selective pressure from an infectious outbreak. We consider a hypothetical population where payoffs from competing wild-type and mutant strategies reflect immune-reproductive trade-offs. Our study shows evolutionary rescue occurs under higher wild-type fecundity and a lower-bounded boost in mutant immunity prolongs the timescale of evolutionary rescue. Higher disease-induced mortality in the wild-type and a larger mutant immunity significantly reinforce the pattern. This model reveals transient synergies between epidemiological and evolutionary dynamics during evolutionary rescue during novel infectious outbreaks.