scholarly journals Bacteria-Bacteriophage Cycles Facilitate Cholera Outbreak Cycles: An Indirect Susceptible - Infected - Bacteria - Phage (Isibp) Model-Based Mathematical Study

2021 ◽  
Author(s):  
Asma Al Habees ◽  
Eman Aldabbas ◽  
Nicola Bragazzi ◽  
Jude Kong
Keyword(s):  
Bacterial Population ◽  
Compartmental Model ◽  
Health Management ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Infectious Agent ◽  
Sensitivity Analyses ◽  
And Control ◽  
Disease Free ◽  
Phage Population

Cholera is an acute enteric infectious disease caused by the Gram-negative bacterium Vibrio Cholerae. Despite a huge body of research, the precise nature of its transmission dynamics has yet to be fully elucidated. Mathematical models can be useful to better understand how an infectious agent can spread and be properly controlled. We develop a compartmental model describing a Human population, a bacterial population as well as a phage population. We show that there might be eight equilibrium points; one of which is a disease free equilibrium point. We carry out numerical simulations and sensitivity analyses and we show that the presence of phage can reduce the number of infectious individuals. Moreover, we discuss the main implications in terms of public health management and control strategies.

Monitoring, Diagnostics, and Prognostics for Robot Tool Center Accuracy Degradation

2018 ◽  
Author(s):  
Guixiu Qiao ◽  
Brian A. Weiss
Keyword(s):  
Health Management ◽  
Control Strategies ◽  
Test Methods ◽  
Component Level ◽  
Data Set ◽  
Root Cause ◽  
Robot Systems ◽  
Robot Performance ◽  
And Control ◽  
Constituent Elements

Over time, robots degrade because of age and wear, leading to decreased reliability and increasing potential for faults and failures; this negatively impacts robot availability. Economic factors motivate facilities and factories to improve maintenance operations to monitor robot degradation and detect faults and failures, especially to eliminate unexpected shutdowns. Since robot systems are complex, with sub-systems and components, it is challenging to determine these constituent elements’ specific influence on the overall system performance. The development of monitoring, diagnostic, and prognostic technologies (collectively known as Prognostics and Health Management (PHM)), can aid manufacturers in maintaining the performance of robot systems by providing intelligence to enhance maintenance and control strategies. This paper presents the strategy of integrating top level and component level PHM to detect robot performance degradation (including robot tool center accuracy degradation), supported by the development of a four-layer sensing and analysis structure. The top level PHM can quickly detect robot tool center accuracy degradation through advanced sensing and test methods developed at the National Institute of Standards and Technology (NIST). The component level PHM supports deep data analysis for root cause diagnostics and prognostics. A reference data set is collected and analyzed using the integration of top level PHM and component level PHM to understand the influence of temperature, speed, and payload on robot’s accuracy degradation.

Hierarchical Decomposition of a Manufacturing Work Cell to Promote Monitoring, Diagnostics, and Prognostics

2017 ◽  
Author(s):  
Brian A. Weiss ◽  
Guixiu Qiao
Keyword(s):  
Machine Tools ◽  
Health Management ◽  
Control Strategies ◽  
Industrial Robot ◽  
Work Cell ◽  
Critical Elements ◽  
Functional Relationships ◽  
Manufacturing Operations ◽  
Robot Systems ◽  
And Control

Manufacturing work cell operations are typically complex, especially when considering machine tools or industrial robot systems. The execution of these manufacturing operations require the integration of layers of hardware and software. The integration of monitoring, diagnostic, and prognostic technologies (collectively known as prognostics and health management (PHM)) can aid manufacturers in maintaining the performance of machine tools and robot systems by providing intelligence to enhance maintenance and control strategies. PHM can improve asset availability, product quality, and overall productivity. It is unlikely that a manufacturer has the capability to implement PHM in every element of their system. This limitation makes it imperative that the manufacturer understand the complexity of their system. For example, a typical robot systems include a robot, end-effector(s), and any equipment, devices, or sensors required for the robot to perform its task. Each of these elements is bound, both physically and functionally, to one another and thereby holds a measure of influence. This paper focuses on research to decompose a work cell into a hierarchical structure to understand the physical and functional relationships among the system’s critical elements. These relationships will be leveraged to identify areas of risk, which would drive a manufacturer to implement PHM within specific areas.

scholarly journals TRANSMISSION DYNAMICS OF DENGUE IN COSTA RICA: THE ROLE OF HOSPITALIZATIONS

2019 ◽  
Vol 27 (1) ◽  
pp. 241-266
Author(s):  
FABIO SANCHEZ ◽  
JORGE ARROYO-ESQUIVEL ◽  
PAOLA VÁSQUEZ
Keyword(s):  
Costa Rica ◽  
Compartmental Model ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Specific Parameter ◽  
Public Health Officials ◽  
Disease Free

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals in the transmission dynamics of dengue in Costa Rica. The basic reproductive number, R0, is computed, as well as a sensitivity analysis on R0 parameters. The global stability of the disease-free equilibrium is established. Numerical simulations under specific parameter scenarios are performed to determine optimal prevention/control strategies.

scholarly journals Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia

2020 ◽  
Author(s):  
Haileyesus Tessema Alemneh ◽  
Getachew Teshome Telahun
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Control Model ◽  
Control Analysis ◽  
Basic Model ◽  
Short Period ◽  
Disease Free

In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagins Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

EXISTENCE OF TRAVELLING WAVES IN NONLINEAR SI EPIDEMIC MODELS

2009 ◽  
Vol 17 (04) ◽  
pp. 643-657 ◽  
Author(s):  
FEN-FEN ZHANG ◽  
GANG HUO ◽  
QUAN-XING LIU ◽  
GUI-QUAN SUN ◽  
ZHEN JIN
Keyword(s):  
Control Strategies ◽  
Travelling Waves ◽  
Equilibrium Points ◽  
Heteroclinic Orbit ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Point Of View ◽  
Spatially Extended ◽  
Theoretical Results ◽  
Disease Free

In this paper, we investigate a spatially extended SI epidemic system with a nonlinear incidence rate. Using mathematical analysis, we study the existence of a heteroclinic orbit connecting two equilibrium points in R3 which corresponds to a travelling wave solution connecting the disease-free and endemic equilibria for the reaction-diffusion system. In other words, the travelling wave solutions of the model are studied to determine the speed of disease dissemination, form the biological point of view. Moreover, this wave speed is obtained as a function of the model's parameters, in order to assess the control strategies. Also, our theoretical results are confirmed by numerical simulations. The obtained results confirm that travelling wave can enhance the spread of the disease, which can provide some insights into controlling the disease.

scholarly journals Dynamics of swine influenza model with optimal control

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Takasar Hussain ◽  
Muhammad Ozair ◽  
Kazeem Oare Okosun ◽  
Muhammad Ishfaq ◽  
Aziz Ullah Awan ◽  
...  
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Swine Influenza ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
And Control ◽  
Disease Free ◽  
Good Agreement

AbstractTransmission dynamics of swine influenza pandemic is analysed through a deterministic model. Qualitative analysis of the model includes global asymptotic stability of disease-free and endemic equilibria under a certain condition based on the reproduction number. Sensitivity analysis to ponder the effect of model parameters on the reproduction number is performed and control strategies are designed. It is also verified that the obtained numerical results are in good agreement with the analytical ones.

scholarly journals Stability analysis of a fractional ordered COVID-19 model

2021 ◽  
Vol 9 (1) ◽  
pp. 22-45 ◽  
Author(s):  
Meghadri Das ◽  
Guruprasad Samanta
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Compartmental Model ◽  
Equilibrium Points ◽  
Real Data ◽  
Transmission Dynamics ◽  
Sensitivity Index ◽  
Limited Information ◽  
First Case ◽  
Disease Free

Abstract The main purpose of this work is to study transmission dynamics of COVID-19 in Italy 2020, where the first case of Coronavirus disease 2019 (COVID-19) in Italy was reported on 31st January 2020. Taking into account the uncertainty due to the limited information about the Coronavirus (COVID-19), we have taken the modified Susceptible-Asymptomatic-Infectious-Recovered (SAIR) compartmental model under fractional order framework. We have formulated our model by subdividing infectious compartment into two sub compartments (reported and unreported) and introduced hospitalized class. In this work, we have studied the local and global stability of the system at different equilibrium points (disease free and endemic) and calculated sensitivity index for Italy scenario. The validity of the model is justified by comparing real data with the results obtained from simulations.

scholarly journals Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Ebrima Kanyi ◽  
Ayodeji Sunday Afolabi ◽  
Nelson Owuor Onyango
Keyword(s):  
Equilibrium Point ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Modeling And Analysis ◽  
Disease Free

This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R 0 , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R 0 > 1 . It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R 0 < 1 , and the unique endemic equilibrium point is locally asymptotically stable whenever R 0 > 1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R 0 = 1 , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R 0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis.

scholarly journals Modeling Peste des Petits Ruminants (PPR) Disease Propagation and Control Strategies Using Memoryless State Transitions

2017 ◽  
Vol 1 (2) ◽  
pp. 90 ◽  
Author(s):  
Michael D. Mitchell ◽  
Walter E. Beyeler ◽  
Patrick Finley ◽  
Melissa Finley DVM, PhD
Keyword(s):  
Empirical Data ◽  
Large Scale ◽  
Control Strategies ◽  
Mitigation Strategies ◽  
Sensitivity Analyses ◽  
Effective Control ◽  
State Transitions ◽  
Morbidity Rate ◽  
Peste Des Petits Ruminants ◽  
And Control

<p><em>Peste des Petits Ruminants (PPR) is an infectious disease affecting goats and sheep. PPR has a mortality rate of 80% and a morbidity rate of 100% in naïve herds. This disease is currently of concern to Afghani goat and sheep herders as conditions in Afghanistan are conducive to the disease becoming an epidemic. PPR is similar to Rinderpest, but is not as well studied. There is a lack of empirical data on how the disease spreads or effective large-scale mitigation strategies. We developed a herd-level, event-driven model of PPR, using memoryless state transitions, to study how the virus propagates through a herd, and to identify effective control strategies for disparate herd configurations and environments. This model allows us to perform Sensitivity Analyses (SA) on environmental and disease parameters for which we do not have empirical data and to simulate the effectiveness of various control strategies. We find that reducing the amount of time from the identification of PPR in a herd to the vaccination of the herd will radically reduce the number of deaths that result from PPR. The goal of this model is to give policy makers a tool to develop effective containment strategies for managing outbreaks of PPR.</em></p>

scholarly journals A Mathematical Model of Treatment and Vaccination Interventions of Pneumococcal Pneumonia Infection Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Mohammed Kizito ◽  
Julius Tumwiine
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
The Elderly ◽  
Infection Dynamics ◽  
And Control ◽  
Long Term Behavior ◽  
The Impact ◽  
Globally Stable ◽  
Disease Free

Streptococcus pneumoniae is one of the leading causes of serious morbidity and mortality worldwide, especially in young children and the elderly. In this study, a model of the spread and control of bacterial pneumonia under public health interventions that involve treatment and vaccination is formulated. It is found out that the model exhibits the disease-free and endemic equilibria. The disease-free equilibrium is stable if and only if the basic reproduction number R0<1 and the disease will be wiped out of the population. For R0≥1, the endemic equilibrium is globally stable and the disease persists. We infer the effect of these interventions on the dynamics of the pneumonia through sensitivity analysis on the effective reproduction number Re, from which it is revealed that treatment and vaccination interventions combined can eradicate pneumonia infection. Numerical simulation to illustrate the analytical results and establish the long term behavior of the disease is done. The impact of pneumonia infection control strategies is investigated. It is revealed that, with treatment and vaccination interventions combined, pneumonia can be wiped out. However, with treatment intervention alone, pneumonia persists in the population.

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