S-shaped curves are ubiquitous in biology especially when it comes to growth of a population or even an individual. Growth models such as the classical Verhulst-Pearl logistic growth equation and its extensions effectively model such S-shaped growth curves. Most of these models are parametrized by three or more parameters. In this work, continued fraction of straight lines has been applied to model S-shaped curves of biological growth through the use of only two parameters a and m. Here, m is the maximum growth rate and a is the parameter restricting the growth rate. The parameters a and m help to better interpret the data when compared to the logistic growth model since m represents factors promoting growth while a represents restricting factors of growth. This model is effective for modeling both population as well as individual growth, especially around the phase of rapid growth.

I present a new dose-survival equation for fitting clonogenic assay data collected for irradiated cells, one motivated by the hypothesis that all cellular activities can be partitioned into two states (“state R” and “state Q”) which differ in their sensitivity to low-LET radiation. The LQ model can be derived from it by taking a Taylor expansion. The empirical observation that rapidly proliferating cancer cells have a straighter dose-survival relationship, while slowly proliferating cancer cells and normal cells have a curvier one featuring a shoulder region, is explained in terms of state R and state Q. The new equation (1) provides a convention for classifying cells as radioresistant, (2) provides a means of reducing, or possibly eliminating, cell cycle phase as a variable in treatment outcome, and (3) may enable standardization of the results reported for clonogenic assays. Finally, a novel hypothesis is offered for the “oxygen enhancement ratio” phenomenon.

Mathematical modeling can perform a decisive task in understanding, controlling, and preventing the transmission of infectious diseases by forecasting their spread, estimating the effectiveness of intervention measures, and updating public health policies. A mathematical epidemic model is a vital tool that can mock up the spread of infections under different scenarios and environments, allowing researchers to test and refine their understanding of the fundamental mechanisms. This paper attempts to review some existing mathematical compartmental epidemic models and explore the impact of meteorological factors such as air temperature, humidity, and wind speed on epidemiology. The goal is to identify and categorize key components, research trends, major findings, and gaps within the models. Additionally, the paper discusses some strategies to address these gaps and proposes a compartmental augmentation of the SEIR model incorporating meteorological factors for further work.

This study applies a graph-theoretic framework to analyze the structural dynamics of codon networks derived from SARS-CoV-2 spike protein sequences. By employing a dual-level analysis of Minimum Connected Dominating Sets (MCDS) and community structures, we explore the mathematical underpinnings of viral protein organization. First, we construct the MCDS to identify critical codons that ensure global network connectivity, providing key insights into structurally significant regions of the protein sequence. Next, we analyze the community structures within the network to determine localized structural and functional roles, facilitating the identification of specialized codon groups. Centrality measures are employed to quantify the significance of codons within both the MCDS and the identified communities, highlighting their roles in maintaining network integrity. Furthermore, we investigate the impact of mutations across SARS-CoV-2 variants, assessing their influence on codon connectivity and functional stability. A statistical analysis of MCDS and community node variability provides deeper insights into the structural robustness of the spike protein. This study underscores the potential of mathematical modeling in virology and highlights essential codons as potential targets for therapeutic intervention.

This work constructs a generic model for chemo-immunotherapy of cancer in a healthy tissue. The main interests are the modeling and computer study of chemotherapy, immunotherapy and the advantages in their combined applications. It describes the dynamics of Healthy, Immune, and Cancer cells when chemotherapy and immunotherapy are applied, either separately or combined. The analysis of the model shows that its solutions exist, are bounded and nonnegative on each finite time interval, and thus are biologically feasible. The model simulations describe the development of the disease without intervention, when only chemotherapy or immunotherapy are administered periodically, when the two modalities are combined. In this manner, once validated, the model can be used to design treatment schedules for improved outcomes.

In this work, we investigate the existence of multistationarity for a triple-site mixed phosphorylation network, where the phosphorylation part contains distributive and processive components, while the dephosphorylation part is purely distributive. We obtain a simple inequality which defines a region in parameter space such that the parametric ordinary differential equations (ODE) system modeling the mixed network is multistationary, i.e., it has multiple positive steady states. We obtain a sufficient condition for uniqueness of the steady state in the form of parametric inequalities. Lastly, we show that the emergence of multistationarity is enabled by the catalytic constants regardless of the position of the processive part in the triple-site mixed mechanism phosphorylation network.

The formation of stenosis in the lumen obstructs the normal flow and causes disorders in the cardiovascular system, which becomes riskier due to the curvature of the artery. The curvature affects the blood flow system directly by reducing the velocity, which helps increase the thickness of the stenosis. In this article, the effect of curvature on the stenosed part of an artery is studied using the Navier-Stokes equation in cylindrical polar form. A new model is developed by incorporating a term in quadratic form to address the joint effect of stenosis and curvature upon flow parameters. This model equation with appropriate boundary conditions is solved to get analytical solutions for velocity, volumetric flow rate, pressure drop ratio, and shear stress ratio, and all the results are analyzed geometrically. The results show that when the curvature increases, the pressure drop ratio and shear stress ratio increase, while the velocity and volumetric flow rate decrease. Quantitative effect of the curvature on flow parameters is visualized which may help researchers in the related field.

By considering the recently introduced SIRU model, in this paper we study the dynamic of COVID-19 pandemic under the temporally varying public intervention in the Chilean context. More precisely, we propose a method to forecast cumulative daily reported cases CR(t), and a systematic way to identify the unreported daily cases given CR(t) data. We firstly base on the recently introduced epidemic model SIRU (Susceptible, Asymptomatic Infected, Reported infected, Unreported infected), and focus on the transmission rate parameter τ. To understand the dynamic of the data, we extend the scalar τ to an unknown function τ(t) in the SIRU system, which is then inferred directly from the historical CR(t) data, based on nonparametric estimation. The estimation of τ(t) leads to the estimation of other unobserved functions in the system, including the daily unreported cases. Furthermore, the estimation of τ(t) allows us to build links between the pandemic evolution and the public intervention, which is modeled by logistic regression. We then employ polynomial approximation to construct a predicted curve which evolves with the latest trend of CR(t). In addition, we regularize the evolution of the forecast in such a way that it corresponds to the future intervention plan based on the previously obtained link knowledge. We test the proposed predictor on different time windows. The promising results show the effectiveness of the proposed methods.

We develop a within-host mathematical model for hepatitis B virus infection that leads to hepatocellular carcinoma incorporating immunotherapy as an intervention strategy and also demonstrating drug effects in the sub-therapeutic, therapeutic and toxicity regions of concentration. The model includes the dynamics of hepatocytes, immune cells, cytokines and hepatitis B virus dynamics using a system of ordinary differential equations. Model parameters were estimated using the flexible modeling environment algorithm. Treatment was presented replicating realistic pharmacokinetics of a drug called Nivolumab as a monoclonal antibody type of immunotherapy. Results suggests that immunotherapy reduces the growth of cancer cells when the drug concentration is in a therapeutic region but complete eradication is not possible. Drug concentration above the therapeutic region reduced the cancer cells to better levels but this benefit is associated with toxicity of the drug. Drug concentration below the therapeutic region is associated with little reduction in cancer cells.

This work constructs, analyzes and simulates the SIR-IH model, a modified SIR epidemiological model for the spread of a disease, in which the infection rate and hospitalization ratio are system variables. The motivation, in part, of making the infection rate a state variable comes from the observations that the infectivity of a disease, such as COVID-19, has been changing with the evolution of the disease, and not necessarily by the appearance of new variants. Moreover, it may change in time if more than one variant are present. The addition of a hospitalization rate is done to make the model more applied for those who need to make decisions on the preparedness of the health system, in particular the hospitals, in case of a pandemic. The model consists of a coupled system of differential equations, and its analysis shows the existence, positivity and boundedness of the solutions. Then, computer simulations depict some typical or interesting dynamic behaviors, and the way the system approaches the steady states.