Biomath

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.

Janice Moore

Meir Shillor

BIOMATH

A modified SIR model with dependent infection and hospitalization rates

依赖感染率和住院率的修正SIR模型

This article proposes a model for a ligand molecule binding inside of a protein macromolecule. The model considers peculiarities of the ligand access to a buried binding center of the protein. The number of the ligand molecule possible trajectories inside of an access channel leading to the binding center is limited by the channel. Therefore average velocity of the ligand molecule translocation inside of an access channel increase with the decreasing of its inner diameter. Thus during overcoming of the activation barrier between neighboring balanced positions inside of the channel, the ligand molecule should dissipate certain amount of its energy. In other words it should also overcome a drag barrier of activation, which is thus a component of the activation barrier. Our calculation showed that the drag barrier of activation is proportional to the temperature and to the squared ratio of the ligand diameter and the distance-averaged channel diameter. Due to possible gradient of the channel inner diameter the drag barriers of activation for the forward and backward ligand translocations inside of the channel may not equal one another. It follows from this that the binding constant depends also on the channel shape.

Oleh Pundyak

Some possible peculiarities of a ligand molecule binding inside of a protein macromolecule

配体分子在蛋白质大分子内部结合的一些可能特性

We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach isВ based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused byВ Bundibugyo ebolavirusВ in city of Isiro, Demo- cratic Republic of the Congo. The branching process model allows for a direct comparison of disease transmission across different environments, such as the general community or the Ebola treatment unit. However, the survival model appears to yield parameter estimates with more accuracy and better precision in some circumstances.

Boseung Choi

Sydney Busch

Dieudonne Kazadi

Benoit Kebela

Emile Okitolonda

Yi Dai

Robert M Lumpkin

Wasiur Rahman Khuda Bukhsh

Omar Saucedo

Marcel Yotebieng

Joe Tien

Eben B Kenah

Grzegorz A Rempala

Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC

建模疫情数据：对刚果民主共和国2012年埃博拉病毒病疫情的分析

In this paper we propose a nonlinear reaction-diffusion system describing the interaction between toxin-producing phytoplankton and fish population. We analyze the effect of self- and cross-diffusion on the dynamics of the system. The existence, uniqueness and uniform boundedness of solutions are established in the positive octant. The system is analyzed for various interesting dynamical behaviors which include boundedness, persistence, local stability, global stability around each equilibrium based on some conditions on self- and cross-diffusion coefficients. The analytical findings are verified by numerical simulation.

Hamidou Ouedraogo

Wendkouni Ouedraogo

Boureima Sangare

Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion

毒素-浮游植物-鱼类模型的自扩散与交叉扩散数学分析

Optimal control problems in mathematical epidemiology are often solved by Hamiltonian methods. However, these methods require conditions on the problem to guarantee that they give global solutions. Because of the improved computational power of modern computers, numerical approximate solutions that systematically try a large number of possibilities have become practical. In this paper we give an efficient implementation of an enumerative numerical solution method for an optimal control problem, which applies to cases where standard methods cannot guarantee global optimality. We demonstrate the method on a model where vaccination and treatment are used to control the level of prevalence of an infectious disease. We describe the solution algorithm in detail, and verify the method with simulations. We verify that the enumerative numerical method produces solutions that are locally optimal.

Vianney Mbatumutima

Christopher Thron

Leonard Todjihounde

Enumerative numerical solution for optimal control using treatment and vaccination for an SIS epidemic model

使用治疗和疫苗接种的SIS传染病模型的最优控制枚举数值解法

Arterial stenosis is the thickening of the arterial wall due to the growth of aberrant tissues that prevent adequate blood flow in the human circulatory system and induces cardiovascular diseases. Mild stenosis, may lead to serious or permanent damage if remains uncured. There are differences in the curvature response and material composition between the outer layers and the core. There are several locations in blood vessels where they are curved, which affects the blood flow and shear stress. The Navier-Stokes equation in the cylindrical polar coordinate system has been extended by incorporating curvature term in two-layered blood flow along the axial direction with appropriate boundary conditions. Mathematical expressions for hemodynamic parameters such as velocity profile, volumetric flow rate, pressure drop, and shear stress have been calculated analytically in the case of a curve artery with stenosis. Moreover, we have analyzed the effect of stenosis on different hemodynamic parameters with the variation of core and peripheral-layer viscosity and curvature. Flow quantities are affected by the habitancy of stenosis and stipulate different blood flow behavior in both layers in the case of curved artery. This modeling technique may help researchers in medicine, mathematical biology, and bio-engineering.

Chudamani Pokharel

Pushpa N. Gautam

Chet R. Bhatta

Jeevan Kafle

Analysis of hemodynamic parameters on two-layered blood flow in a curved artery

弯曲动脉中双层血液流动的血液动力学参数分析

We consider the acetogenesis and hydrogenotrophic methanogenesis phases of the anaerobic digestion model and we include the inhibition of methanogenics, first by volatile fatty acids (VFAs) then by acetogenics. We investigate mathematically the dynamics of two chemostat models described by systems of four nonlinear ordinary differential equations. We established the conditions of existence and stability of equilibrium points in each of the models with respect to the dilution rate. The operating diagrams allowed to reveal the similarities and the differences between regions of stability of the two models and to present the consequent transcritical bifurcations between boundary and positive equilibrium. Models are equivalent for low inlet substrate concentration and significantly different for high concentration. When inhibition is by acetogens and for high concentrations of inlet substrate, the upstream species tends to eliminate the downstream species from the vessel.

Nabil Ben Ali

Nahla Abdellatif

Comparative analysis of two chemostat models including substrate and biomass inhibitions

两种包含底物和生物量抑制的恒化器模型的比较分析

Stability analysis of nonlinear age-of-infection and -immunity structured SVLIAR-type model of susceptible, vaccinated, latent, COVID-19 infected, asymptomatic and recovered sub-classes of population dynamics is carried out in this paper. The SVLIAR model uses five age variables - age of vaccine immunity of vaccinated individuals, age of virus infection in organism during incubation period of latent individuals, “age” of infectious disease treatment of infected individuals, age of asymptomatic infectious dis-ease of asymptomatic individuals, “age” of immunity of organism after recovering of recovered individuals. Individuals can move from one subclass to another when these age variables take some fixed values, that is the processes in sub-classes are adjusted and synchronized by age variables. The conditions for the existence of disease-free and unique endemic equilibria and their local asymptotic stability were obtained. The local asymptotic stability/instability of endemic equilibrium of SVLIAR model is defined by criterion, which relates the demographic characteristics of population, infection disease characteristics (disease-induced death rate, death rate induced by the complications after disease), characteristics of vaccination (fraction of fully vaccinated susceptibles per unit of time, vaccination efficacy) and characteristics of age variables (their maximum values) of sub-classes. These theoretical results help understand better the conditions of transmission dynamics of the COVID-19 induced disease.

Vitalii V. Akimenko

SVLIAR age-of-infection and -immunity structured epidemic model of COVID-19 dynamics

SVLIAR 感染年龄和免疫年龄结构的 COVID-19 流行病动力学模型

Publication Information	Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2019，Proportion of original research papers: 0.00%，Self Citation Rate:N.A.， Gold OA Rate: 0.00%
Average review cycle	网友分享经验：20 Weeks

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A modified SIR model with dependent infection and hospitalization rates

Some possible peculiarities of a ligand molecule binding inside of a protein macromolecule

Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC

Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion

Enumerative numerical solution for optimal control using treatment and vaccination for an SIS epidemic model

A modified SIR model with dependent infection and hospitalization rates

Some possible peculiarities of a ligand molecule binding inside of a protein macromolecule

Analysis of hemodynamic parameters on two-layered blood flow in a curved artery

Comparative analysis of two chemostat models including substrate and biomass inhibitions

SVLIAR age-of-infection and -immunity structured epidemic model of COVID-19 dynamics

ISSN	1314-684X, 1314-7218
h-index	6