scholarly journals Global dynamics for a Filippov system with media effects

2022 ◽  
Vol 19 (3) ◽  
pp. 2835-2852
Author(s):  
Cunjuan Dong ◽  
◽  
Changcheng Xiang ◽  
Wenjin Qin ◽  
Yi Yang ◽  
...  
Keyword(s):  
Disease Transmission ◽  
Media Coverage ◽  
Equilibrium Points ◽  
Disease Outbreaks ◽  
Global Dynamics ◽  
Threshold Strategy ◽  
Infectious Disease Outbreaks ◽  
Boundary Equilibrium ◽  
The Stability ◽  
And Control

<abstract><p>In the process of spreading infectious diseases, the media accelerates the dissemination of information, and people have a deeper understanding of the disease, which will significantly change their behavior and reduce the disease transmission; it is very beneficial for people to prevent and control diseases effectively. We propose a Filippov epidemic model with nonlinear incidence to describe media's influence in the epidemic transmission process. Our proposed model extends existing models by introducing a threshold strategy to describe the effects of media coverage once the number of infected individuals exceeds a threshold. Meanwhile, we perform the stability of the equilibriua, boundary equilibrium bifurcation, and global dynamics. The system shows complex dynamical behaviors and eventually stabilizes at the equilibrium points of the subsystem or pseudo equilibrium. In addition, numerical simulation results show that choosing appropriate thresholds and control intensity can stop infectious disease outbreaks, and media coverage can reduce the burden of disease outbreaks and shorten the duration of disease eruptions.</p></abstract>

scholarly journals Analysing livestock network data for infectious disease control: an argument for routine data collection in emerging economies

2019 ◽  
Vol 374 (1776) ◽  
pp. 20180264 ◽  
Author(s):  
G. L. Chaters ◽  
P. C. D. Johnson ◽  
S. Cleaveland ◽  
J. Crispell ◽  
W. A. de Glanville ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Disease Control ◽  
Disease Transmission ◽  
Disease Outbreaks ◽  
Routine Data ◽  
Contact Layer ◽  
Theme Issue ◽  
Targeted Interventions ◽  
Infectious Disease Outbreaks ◽  
And Control

Livestock movements are an important mechanism of infectious disease transmission. Where these are well recorded, network analysis tools have been used to successfully identify system properties, highlight vulnerabilities to transmission, and inform targeted surveillance and control. Here we highlight the main uses of network properties in understanding livestock disease epidemiology and discuss statistical approaches to infer network characteristics from biased or fragmented datasets. We use a ‘hurdle model’ approach that predicts (i) the probability of movement and (ii) the number of livestock moved to generate synthetic ‘complete’ networks of movements between administrative wards, exploiting routinely collected government movement permit data from northern Tanzania. We demonstrate that this model captures a significant amount of the observed variation. Combining the cattle movement network with a spatial between-ward contact layer, we create a multiplex, over which we simulated the spread of ‘fast’ ( R 0 = 3) and ‘slow’ ( R 0 = 1.5) pathogens, and assess the effects of random versus targeted disease control interventions (vaccination and movement ban). The targeted interventions substantially outperform those randomly implemented for both fast and slow pathogens. Our findings provide motivation to encourage routine collection and centralization of movement data to construct representative networks. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’. This theme issue is linked with the earlier issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’.

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals Dot map cartograms for detection of infectious disease outbreaks: an application to Q fever, the Netherlands and pertussis, Germany

2017 ◽  
Vol 22 (26) ◽  
Author(s):  
Loes Soetens ◽  
Susan Hahné ◽  
Jacco Wallinga
Keyword(s):  
Infectious Disease ◽  
The Netherlands ◽  
Q Fever ◽  
Disease Outbreaks ◽  
Point Pattern ◽  
Infectious Disease Outbreaks ◽  
Public Health Professionals ◽  
Potential Source ◽  
High Incidence ◽  
And Control

Geographical mapping of infectious diseases is an important tool for detecting and characterising outbreaks. Two common mapping methods, dot maps and incidence maps, have important shortcomings. The former does not represent population density and can compromise case privacy, and the latter relies on pre-defined administrative boundaries. We propose a method that overcomes these limitations: dot map cartograms. These create a point pattern of cases while reshaping spatial units, such that spatial area becomes proportional to population size. We compared these dot map cartograms with standard dot maps and incidence maps on four criteria, using two example datasets. Dot map cartograms were able to illustrate both incidence and absolute numbers of cases (criterion 1): they revealed potential source locations (Q fever, the Netherlands) and clusters with high incidence (pertussis, Germany). Unlike incidence maps, they were insensitive to choices regarding spatial scale (criterion 2). Dot map cartograms ensured the privacy of cases (criterion 3) by spatial distortion; however, this occurred at the expense of recognition of locations (criterion 4). We demonstrate that dot map cartograms are a valuable method for detection and visualisation of infectious disease outbreaks, which facilitates informed and appropriate actions by public health professionals, to investigate and control outbreaks.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

scholarly journals The Effects of Media Coverage on the Dynamics of Disease in Prey-Predator Model

2021 ◽  
pp. 981-996
Author(s):  
Walaa Madhat Alwan ◽  
Huda Abdul Satar
Keyword(s):  
Media Coverage ◽  
Global Dynamics ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Proposed Model ◽  
Disease In Predator ◽  
Predator Model ◽  
The Stability ◽  
Effects Of Media ◽  
Disease In Prey

In this paper, an eco-epidemiological model with media coverage effects is established and studied. An -type of disease in predator is considered.  All the properties of the solution of the proposed model are discussed. An application to the stability theory was carried out to investigate the local as well as global stability of the system. The persistence conditions of the model are determined. The occurrence of local bifurcation in the model is studied. Further investigation of the global dynamics of the model is achieved through using a numerical simulation.

scholarly journals Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network

2021 ◽  
Vol 19 (2) ◽  
pp. 1677-1695
Author(s):  
Boli Xie ◽  
◽  
Maoxing Liu ◽  
Lei Zhang
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Virus Transmission ◽  
Population Heterogeneity ◽  
Multiple Equilibrium ◽  
Optimal Control Strategy ◽  
Treatment Function ◽  
The Stability ◽  
The Impact

<abstract><p>In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} &lt; 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.</p></abstract>

Mathematical Modeling and Stability Analysis of Japanese Encephalitis

2020 ◽  
Vol 12 (1) ◽  
pp. 120-127
Author(s):  
Vinod Baniya ◽  
Ram Keval
Keyword(s):  
Mathematical Modeling ◽  
Japanese Encephalitis ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Numerical Verification ◽  
Transmission Potential ◽  
Dynamical Behaviors ◽  
Proposed Model ◽  
The Stability ◽  
Stability Issues

Mathematical modeling of Japanese encephalitis (JE) disease in human population with pig and mosquito has been presented in this paper. The proposed model, which involves three compartments of human (Susceptible, Vaccinated, Infected), two compartments of mosquito (Susceptible, Infected) and three compartments of the pig (Susceptible, Vaccinated, Infected). In this work, it is assumed that JE spreads between susceptible class and infected mosquitoes only. Basic results like boundedness of the model, the existence of equilibrium and local stability issues are investigated. Here, to measure the disease transmission potential in the population the basic reproduction number (R0) from the system has been analyzed w.r.t. control parameters both numerically and theoretically. The dynamical behaviors of the system have been analyzed by using the stability theory of differential equations and numerical simulations at equilibrium points. A numerical verification of results is carried out of the model under consideration.

scholarly journals Public perceptions of COVID-19 in Australia: perceived risk, knowledge, health-protective behaviours, and vaccine intentions

2020 ◽  
Author(s):  
Kate Faasse ◽  
Jill Newby
Keyword(s):  
Media Coverage ◽  
Perceived Risk ◽  
Online Survey ◽  
Early Stage ◽  
Disease Outbreaks ◽  
Asymptomatic Infection ◽  
Demographic Groups ◽  
Infectious Disease Outbreaks ◽  
Novel Coronavirus ◽  
Protective Behaviours

AbstractWidespread and sustained engagement with health-protective behaviours (i.e., hygiene and distancing) is critical to successfully managing the COVID-19 pandemic. Evidence from previous emerging infectious disease outbreaks points to the role of perceived risk, worry, media coverage, and knowledge in shaping engagement with health-protective behaviours as well as vaccination intentions. The current study examined these factors in 2,174 Australian residents. An online survey was completed between 2-9 March 2020, at an early stage of the COVID-19 outbreak in Australia. Results revealed that two thirds of respondents were at least moderately worried about a widespread COVID-19 outbreak in Australia (which subsequently occurred). Worry about the outbreak and closely following media coverage were consistent predictors of health-protective behaviours (both over the previous month, and intended behaviours in the case of a widespread outbreak) as well as vaccination intentions. Health-behaviour engagement over the previous month was lower in some demographic groups, including males and younger individuals (18-29 age group). These was a substantial mismatch between respondents’ expected symptoms of infection and emerging evidence that a meaningful proportion of people who contract the novel coronavirus will experience asymptomatic infection (i.e., they will not experience symptoms associated with COVID-19). Only 0.3% of those in the current study believed that they personally would not experience any symptoms if they were infected. Uncertainty and misconceptions about COVID-19 were common, including one third of respondents who reported being unsure whether people are likely have natural or existing immunity. There was also uncertainty around whether specific home remedies (e.g., vitamins, saline rinses) would offer protection, whether the virus could spread via the airborne route, and whether the virus was human made and deliberately released. Such misconceptions are likely to cause concern for members of the public. These results point to areas of uncertainty that could be usefully targeted by public education campaigns, as well as psychological and demographic factors associated with engagement with health-protective behaviours. These findings offer potential pathways for interventions to encourage health-protective behaviours to reduce the spread of COVID-19.

scholarly journals Optimizing spatial and seasonal deployment of vaccination campaigns to eliminate wildlife rabies

2019 ◽  
Vol 374 (1776) ◽  
pp. 20180280 ◽  
Author(s):  
Laurie Baker ◽  
Jason Matthiopoulos ◽  
Thomas Müller ◽  
Conrad Freuling ◽  
Katie Hampson
Keyword(s):  
Infectious Disease ◽  
Plant Pathogens ◽  
Herd Immunity ◽  
Disease Outbreaks ◽  
Vaccination Strategy ◽  
Theme Issue ◽  
Infectious Disease Outbreaks ◽  
Control Programmes ◽  
The Face ◽  
And Control

Understanding how the spatial deployment of interventions affects elimination time horizons and potential for disease re-emergence has broad application to control programmes targeting human, animal and plant pathogens. We previously developed an epidemiological model that captures the main features of rabies spread and the impacts of vaccination based on detailed records of fox rabies in eastern Germany during the implementation of an oral rabies vaccination (ORV) programme. Here, we use simulations from this fitted model to determine the best vaccination strategy, in terms of spatial placement and timing of ORV efforts, for three epidemiological scenarios representative of current situations in Europe. We found that consecutive and comprehensive twice-yearly vaccinations across all regions rapidly controlled and eliminated rabies and that the autumn campaigns had the greater impact on increasing the probability of elimination. This appears to result from the need to maintain sufficient herd immunity in the face of large birth pulses, as autumn vaccinations reach susceptible juveniles and therefore a larger proportion of the population than spring vaccinations. Incomplete vaccination compromised time to elimination requiring the same or more vaccination effort to meet similar timelines. Our results have important practical implications that could inform policies for rabies containment and elimination in Europe and elsewhere. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’. This theme issue is linked with the earlier issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’.

scholarly journals Perfect counterfactuals for epidemic simulations

2019 ◽  
Vol 374 (1776) ◽  
pp. 20180279 ◽  
Author(s):  
Joshua Kaminsky ◽  
Lindsay T. Keegan ◽  
C. Jessica E. Metcalf ◽  
Justin Lessler
Keyword(s):  
Infectious Disease ◽  
Disease Outbreaks ◽  
Computation Time ◽  
Control Measures ◽  
Mathematical Representation ◽  
Theme Issue ◽  
Stochastic Variation ◽  
Infectious Disease Outbreaks ◽  
Negative Effect ◽  
And Control

Simulation studies are often used to predict the expected impact of control measures in infectious disease outbreaks. Typically, two independent sets of simulations are conducted, one with the intervention, and one without, and epidemic sizes (or some related metric) are compared to estimate the effect of the intervention. Since it is possible that controlled epidemics are larger than uncontrolled ones if there is substantial stochastic variation between epidemics, uncertainty intervals from this approach can include a negative effect even for an effective intervention. To more precisely estimate the number of cases an intervention will prevent within a single epidemic, here we develop a ‘single-world’ approach to matching simulations of controlled epidemics to their exact uncontrolled counterfactual. Our method borrows concepts from percolation approaches, prunes out possible epidemic histories and creates potential epidemic graphs (i.e. a mathematical representation of all consistent epidemics) that can be ‘realized’ to create perfectly matched controlled and uncontrolled epidemics. We present an implementation of this method for a common class of compartmental models (e.g. SIR models), and its application in a simple SIR model. Results illustrate how, at the cost of some computation time, this method substantially narrows confidence intervals and avoids nonsensical inferences. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’. This theme issue is linked with the earlier issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’.

Sign in / Sign up

Export Citation Format

Share Document