Some models with repulsion effect on superinfecting viruses by infected cells

2019 ◽  
Vol 12 (07) ◽  
pp. 1950079
Author(s):  
Jun-Feng Li
Keyword(s):  
Production Rate ◽  
Death Rate ◽  
Equilibrium Solution ◽  
Reproduction Number ◽  
Constant Solution ◽  
Number Formula ◽  
Free Constant ◽  
Infected Cells ◽  
The Stability ◽  
Repulsion Effect

In this paper, we study some models with repulsion effect on superinfecting viruses by infected cells [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are the density of uninfected cells, infected cells and viruses at time [Formula: see text] at location [Formula: see text], respectively. The functions [Formula: see text] and [Formula: see text] are assumed to be positive, continuous and bounded. [Formula: see text] denotes the production rate of uninfected cells. The infection rate is [Formula: see text] and the function [Formula: see text] is the production rate of free viruses. And [Formula: see text] is the rate of transfer from uninfected cells to infected cells. The positive constants [Formula: see text] and [Formula: see text] denote the death rate of uninfected cells, infected cells and viruses, respectively. The stability of the infection-free equilibrium solution and infection equilibrium solution is discussed. It is shown that if the basic reproduction number [Formula: see text] then the chemotaxis has no effect, that is, the infection-free constant solution is stable. For the system with chemotactic sensitivity [Formula: see text], if [Formula: see text], then the infection constant solution will be unstable under some conditions.

Global dynamics in an age-structured HIV model with humoral immunity

2021 ◽  
pp. 2150047
Author(s):  
Zhongzhong Xie ◽  
Xiuxiang Liu
Keyword(s):  
Differential Equations ◽  
Humoral Immunity ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Hiv Model ◽  
Infection Age ◽  
Number Formula ◽  
Infected Cells ◽  
Age Structured ◽  
Disease Free

In this paper, we formulate an age-structured HIV model, in which the influence of humoral immunity and the infection age of the infected cells are considered. The model is governed by three ordinary differential equations and two first-ordered partial differential equations and admits three equilibria: disease-free, immune-inactivated and immune-activated equilibria. We introduce two important thresholds: the basic reproduction number [Formula: see text] and immune-activated reproduction number [Formula: see text] and further show the global stability of above three equilibria in terms of [Formula: see text] and [Formula: see text], respectively. The numerical simulations are presented to illustrate our results.

Assessing the impact of transmissibility on a cluster-based COVID-19 model in India

2021 ◽  
pp. 2141002
Author(s):  
Tanvi ◽  
Mohammad Sajid ◽  
Rajiv Aggarwal ◽  
Ashutosh Rajput
Keyword(s):  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Nonlinear Mathematical Model ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
The Stability ◽  
The Impact ◽  
Disease Free

In this paper, we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus (COVID-19). The model incorporates the effect of transmission and treatment on the occurrence of new infections. For the model, the basic reproduction number [Formula: see text] has been computed. Corresponding to the threshold quantity [Formula: see text], the stability of endemic and disease-free equilibrium (DFE) points are determined. For [Formula: see text], if the endemic equilibrium point exists, then it is locally asymptotically stable, whereas the DFE point is globally asymptotically stable for [Formula: see text] which implies the eradication of the disease. The effects of various parameters on the spread of COVID-19 are discussed in the segment of sensitivity analysis. The model is numerically simulated to understand the effect of reproduction number on the transmission dynamics of the disease COVID-19. From the numerical simulations, it is concluded that if the reproduction number for the coronavirus disease is reduced below unity by decreasing the transmission rate and detecting more number of infectives, then the epidemic can be eradicated from the population.

Stability of a Time Delayed SIR Epidemic Model Along with Nonlinear Incidence Rate and Holling Type-II Treatment Rate

2018 ◽  
Vol 15 (06) ◽  
pp. 1850055 ◽  
Author(s):  
Abhishek Kumar ◽  
Nilam
Keyword(s):  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Type Ii ◽  
Treatment Rate ◽  
Nonlinear Incidence Rate ◽  
Number Formula ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we present a mathematical study of a deterministic model for the transmission and control of epidemics. The incidence rate of susceptible being infected is very crucial in the spread of disease. The delay in the incidence rate is proved fatal. In the present study, we propose an SIR mathematical model with the delay in the infected population. We are taking nonlinear incidence rate for epidemics along with Holling type II treatment rate for understanding the dynamics of the epidemics. Model stability has been done by the basic reproduction number [Formula: see text]. The model is locally asymptotically stable for disease-free equilibrium [Formula: see text] when the basic reproduction number [Formula: see text] is less than one ([Formula: see text]). We investigated the stability of the model for disease-free equilibrium at [Formula: see text] equals to one using center manifold theory. We also investigated the stability for endemic equilibrium [Formula: see text] at [Formula: see text]. Further, numerical simulations are presented to exemplify the analytical studies.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals A Theoretical Model for the Transmission Dynamics of the Buruli Ulcer with Saturated Treatment

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ebenezer Bonyah ◽  
Isaac Dontwi ◽  
Farai Nyabadza
Keyword(s):  
Human Population ◽  
Reproduction Number ◽  
Buruli Ulcer ◽  
Coupled System ◽  
Model Parameters ◽  
The Public ◽  
Treatment Function ◽  
Medical Facilities ◽  
The Stability ◽  
Saturated Treatment

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

scholarly journals A Stochastic TB Model for a Crowded Environment

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sibaliwe Maku Vyambwera ◽  
Peter Witbooi
Keyword(s):  
Compartmental Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Equation Model ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
The Stability ◽  
Crowded Environments ◽  
Disease Free

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

Fusion based learning approach for predicting concrete pouring productivity based on construction and supply parameters

2016 ◽  
Vol 16 (2) ◽  
pp. 185-202 ◽  
Author(s):  
Mojtaba Maghrebi ◽  
Ali Shamsoddini ◽  
S. Travis Waller
Keyword(s):  
Supply Chain ◽  
Production Rate ◽  
Learning Method ◽  
Data Set ◽  
Content Type ◽  
Field Database ◽  
The Stability ◽  
Stable Learning ◽  
Ready Mixed Concrete ◽  
Practical Implications

Purpose The purpose of this paper is to predict the concrete pouring production rate by considering both construction and supply parameters, and by using a more stable learning method. Design/methodology/approach Unlike similar approaches, this paper considers not only construction site parameters, but also supply chain parameters. Machine learner fusion-regression (MLF-R) is used to predict the production rate of concrete pouring tasks. Findings MLF-R is used on a field database including 2,600 deliveries to 507 different locations. The proposed data set and the results are compared with ANN-Gaussian, ANN-Sigmoid and Adaboost.R2 (ANN-Gaussian). The results show better performance of MLF-R obtaining the least root mean square error (RMSE) compared with other methods. Moreover, the RMSEs derived from the predictions by MLF-R in some trials had the least standard deviation, indicating the stability of this approach among similar used approaches. Practical implications The size of the database used in this study is much larger than the size of databases used in previous studies. It helps authors draw their conclusions more confidently and introduce more generalised models that can be used in the ready-mixed concrete industry. Originality/value Introducing a more stable learning method for predicting the concrete pouring production rate helps not only construction parameters, but also traffic and supply chain parameters.

The threshold for a stochastic within-host CHIKV virus model with saturated incidence rate

2021 ◽  
pp. 2150042
Author(s):  
C. Gokila ◽  
M. Sambath
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Stationary Distribution ◽  
Reproduction Number ◽  
Threshold Value ◽  
Saturated Incidence Rate ◽  
Number Formula ◽  
Saturated Incidence ◽  
Virus Model ◽  
Global Positive Solution

This paper deals with stochastic Chikungunya (CHIKV) virus model along with saturated incidence rate. We show that there exists a unique global positive solution and also we obtain the conditions for the disease to be extinct. We also discuss about the existence of a unique ergodic stationary distribution of the model, through a suitable Lyapunov function. The stationary distribution validates the occurrence of disease; through that, we find the threshold value for prevail and disappear of disease within host. With the help of numerical simulations, we validate the stochastic reproduction number [Formula: see text] as stated in our theoretical findings.

scholarly journals Posttranscriptional regulation of hsp70 expression in human cells: effects of heat shock, inhibition of protein synthesis, and adenovirus infection on translation and mRNA stability.

1987 ◽  
Vol 7 (12) ◽  
pp. 4357-4368 ◽  
Author(s):  
N G Theodorakis ◽  
R I Morimoto
Keyword(s):  
Protein Synthesis ◽  
Heat Shock ◽  
Posttranscriptional Regulation ◽  
High Efficiency ◽  
Hsp70 Expression ◽  
Mrna Levels ◽  
Protein Synthesis Inhibitors ◽  
Hsp70 Mrna ◽  
Infected Cells ◽  
The Stability

We have examined the posttranscriptional regulation of hsp70 gene expression in two human cell lines, HeLa and 293 cells, which constitutively express high levels of HSP70. HSP70 mRNA translates with high efficiency in both control and heat-shocked cells. Therefore, heat shock is not required for the efficient translation of HSP70 mRNA. Rather, the main effect of heat shock on translation is to suppress the translatability of non-heat shock mRNAs. Heat shock, however, has a marked effect on the stability of HSP70 mRNA; in non-heat-shocked cells the half-life of HSP70 mRNA is approximately 50 min, and its stability increases at least 10-fold upon heat shock. Moreover, HSP70 mRNA is more stable in cells treated with protein synthesis inhibitors, suggesting that a heat shock-sensitive labile protein regulates its turnover. An additional effect on posttranscriptional regulation of hsp70 expression can be found in adenovirus-infected cells, in which HSP70 mRNA levels decline precipititously late during infection although hsp70 transcription continues unabated.

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