SIRS epidemiological model with ratio‐dependent incidence: Influence of preventive vaccination and treatment control strategies on disease dynamics

2021 ◽  
Author(s):  
Udai Kumar ◽  
Partha Sarathi Mandal ◽  
Jai Prakash Tripathi ◽  
Vijay Pal Bajiya ◽  
Sarita Bugalia
Keyword(s):  
Control Strategies ◽  
Epidemiological Model ◽  
Disease Dynamics ◽  
Treatment Control ◽  
Preventive Vaccination ◽  
Ratio Dependent

scholarly journals SIR epidemiological model with ratio-dependent incidence: influence of preventive vaccination and treatment control strategies on disease dynamics

2021 ◽  
Author(s):  
Uday Kumar ◽  
PARTHA MANDAL ◽  
Jai Tripathi ◽  
Sarita Bugalia ◽  
Vijay Pal Bajiya
Keyword(s):  
Control Strategies ◽  
Rate Function ◽  
Model System ◽  
Sir Epidemic Model ◽  
Treatment Rate ◽  
Treatment Control ◽  
Preventive Vaccination ◽  
Ratio Dependent ◽  
The Impact ◽  
Maximal Capacity

In this paper, we study an SIR epidemic model with ratio dependent incident rate function. We explore the impact of vaccination and treatment on the transmission dynamics of the disease. The treatment control strategies depend on the availability of maximal treatment capacity: treatment rate is constant when the number of infected individuals is greater than the maximal capacity of treatment and proportional to the number of infected individuals when the number of infected individuals is less than the maximal capacity of treatment. The existence and stability of the endemic equilibria are governed by the basic reproduction number and treatment control strategies. By carrying out rigorous mathematical analysis and numerical evaluations, it has been shown that (1) the sufficiently large value of the preventive vaccination rate can control the spread of disease, (2) a threshold level of the psychological (or inhibitory) effects in the incidence rate function is enough to decrease the infective population. Model system also undergoes a transcritical and a saddle-node bifurcation with respect to disease contact rate. In the presence of treatment strategies, system have multiple endemic equilibria and undergoes a backward bifurcation. The number of infected individuals decreases with respect to maximal treatment capacity and disease dies out from the system for large capacity of the treatment when constant treatment strategy is applied. Further, it is also found that the spread of disease can be suppressed by increasing treatment rate. Sensitivity analysis shows that the transmission and treatment rates are most sensitive parameters on the model system.

A genetic-epidemiological model for Marek’s Disease in Poultry

2009 ◽  
Vol 2009 ◽  
pp. 197-197
Author(s):  
M Nath ◽  
S C Bishop
Keyword(s):  
Control Strategies ◽  
Epidemiological Model ◽  
Marek's Disease ◽  
Disease Dynamics ◽  
Marek’S Disease ◽  
Parameter Spaces ◽  
Gene Markers ◽  
Poultry Breeding ◽  
Breeding Programmes ◽  
Or Gene

Marek’s disease (MD), caused by a herpes virus, is a very infectious, lymphoproliferative and chronic disease of poultry. Breeding for improved MD resistance poultry stock is possible since MD resistance has been associated with MHC haplotypes, QTL and candidate genes. However, integration of host genetics vis-à-vis other control strategies and the utilisation of genes or gene markers for MD in practical breeding programmes is still a challenge. The objective of the present study was to develop a basic genetic-epidemiological model for Marek’s disease infection in poultry, identify parameter spaces that describe the disease dynamics correctly and investigate the impacts of possible genetic and vaccination control strategies on overall disease dynamics.

scholarly journals Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramziya Rifhat ◽  
Zhidong Teng ◽  
Chunxia Wang
Keyword(s):  
Epidemic Model ◽  
Control Strategies ◽  
Random Perturbations ◽  
Disease Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Analysis Theory ◽  
Lyapunov Function Method ◽  
Random Fluctuations ◽  
Theoretical Results

AbstractIn this paper, a stochastic SIRV epidemic model with general nonlinear incidence and vaccination is investigated. The value of our study lies in two aspects. Mathematically, with the help of Lyapunov function method and stochastic analysis theory, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics. In other words, neglecting random perturbations overestimates the ability of the disease to spread. The numerical simulations are given to illustrate the main theoretical results.

scholarly journals Fighting a fire versus waiting for a wave: Useful and not-so-useful analogies in times of SARS-CoV-2

2021 ◽  
Author(s):  
Louise Archer ◽  
Claire Standley ◽  
Péter Molnár
Keyword(s):  
Public Health ◽  
Control Strategies ◽  
Spatial Dynamics ◽  
Disease Outbreak ◽  
Biological Processes ◽  
Disease Dynamics ◽  
Epidemiological Models ◽  
Communication Tools ◽  
Regular Feature ◽  
News Headlines

As SARS-CoV-2 has swept the planet, intermittent “lockdowns” have become a regular feature to control transmission. References to so-called recurring “waves” of infections remain pervasive among news headlines, political messaging, and public health sources. Here, we consider the power of analogies as a tool for facilitating effective understanding of biological processes by reviewing the successes and limitations of various analogies in the context of the COVID-19 pandemic. We also consider how, when analogies fall short, their ability to persuade can mislead public opinion and behaviour, even if unintentionally. While waves can be effective in conveying patterns of disease outbreak retrospectively, we suggest that process-based analogies might be more effective communication tools, given that they are easily mapped to underlying epidemiological concepts and can be extended to include more complex (e.g., spatial) dynamics. Though no single analogy perfectly captures disease dynamics, fire is particularly suitable for visualizing the epidemiological models that are used to understand disease trajectories, underscoring the importance of and reasoning behind control strategies, and, above all, conveying a sense of urgency to galvanise collective action.

scholarly journals Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Liyan Wang ◽  
Huilin Huang ◽  
Ancha Xu ◽  
Weiming Wang
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Epidemic Model ◽  
Media Coverage ◽  
Control Strategies ◽  
Disease Dynamics ◽  
Unique Positive Solution ◽  
Sirs Epidemic Model ◽  
Deterministic Framework ◽  
Stochastic Extinction

We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of unique positive solution and the stochastic extinction of the SDE model and discuss the exponentialp-stability and global stability of the SDE model. One of the most interesting findings is that if the intensity of noise is large, then the disease is prone to extinction, which can provide us with some useful control strategies to regulate disease dynamics.

scholarly journals Control Intervention Strategies for Within-Host, Between-Host and their Efficacy in the Treatment, Spread of COVID-19 : A Multi Scale Modeling Approach

2020 ◽  
Vol 8 (1) ◽  
pp. 198-210
Author(s):  
D. Bhanu Prakash ◽  
D. K. K. Vamsi ◽  
D. Bangaru Rajesh ◽  
Carani B Sanjeevi
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Population Level ◽  
Scale Model ◽  
Disease Dynamics ◽  
Level Control ◽  
Multi Scale ◽  
Scale Modeling ◽  
Control Intervention ◽  
Combined Strategy

AbstractThe COVID-19 pandemic has resulted in more than 65.5 million infections and 15,14,695 deaths in 212 countries over the last few months. Different drug intervention acting at multiple stages of pathogenesis of COVID-19 can substantially reduce the infection induced, thereby decreasing the mortality. Also population level control strategies can reduce the spread of the COVID-19 substantially. Motivated by these observations, in this work we propose and study a multi scale model linking both within-host and between-host dynamics of COVID-19. Initially the natural history dealing with the disease dynamics is studied. Later comparative effectiveness is performed to understand the efficacy of both the within-host and population level interventions. Findings of this study suggest that a combined strategy involving treatment with drugs such as Arbidol, remdesivir, Lopinavir/Ritonavir that inhibits viral replication and immunotherapies like monoclonal antibodies, along with environmental hygiene and generalized social distancing proved to be the best and optimal in reducing the basic reproduction number and environmental spread of the virus at the population level.

scholarly journals A novel COVID-19 epidemiological model with explicit susceptible and asymptomatic isolation compartments reveals unexpected consequences of timing social distancing

2020 ◽  
Author(s):  
Jana L. Gevertz ◽  
James M. Greene ◽  
Cynthia Sanchez-Tapia ◽  
Eduardo D. Sontag
Keyword(s):  
Disease Transmission ◽  
Control Strategies ◽  
Dynamical Behavior ◽  
Critical Time ◽  
Epidemiological Model ◽  
Appreciable Effect ◽  
Negative Effects ◽  
Social Distancing ◽  
The Impact ◽  
Implementation Delay

AbstractMotivated by the current COVID-19 epidemic, this work introduces an epidemiological model in which separate compartments are used for susceptible and asymptomatic “socially distant” populations. Distancing directives are represented by rates of flow into these compartments, as well as by a reduction in contacts that lessens disease transmission. The dynamical behavior of this system is analyzed, under various different rate control strategies, and the sensitivity of the basic reproduction number to various parameters is studied. One of the striking features of this model is the existence of a critical implementation delay (“CID”) in issuing separation mandates: while a delay of about two weeks does not have an appreciable effect on the peak number of infections, issuing mandates even slightly after this critical time results in a far greater incidence of infection. Thus, there is a nontrivial but tight “window of opportunity” for commencing social distancing in order to meet the capacity of healthcare resources. However, if one wants to also delay the timing of peak infections –so as to take advantage of potential new therapies and vaccines– action must be taken much faster than the CID. Different relaxation strategies are also simulated, with surprising results. Periodic relaxation policies suggest a schedule which may significantly inhibit peak infective load, but that this schedule is very sensitive to parameter values and the schedule’s frequency. Furthermore, we considered the impact of steadily reducing social distancing measures over time. We find that a too-sudden reopening of society may negate the progress achieved under initial distancing guidelines, but the negative effects can be mitigated if the relaxation strategy is carefully designed.

Using disease dynamics and modeling to inform control strategies in low-income countries

2018 ◽  
Author(s):  
Matthew Ferrari
Keyword(s):  
Infectious Disease ◽  
Low Income ◽  
Dynamic Models ◽  
Control Strategies ◽  
Disease Incidence ◽  
Herd Immunity ◽  
Unintended Consequences ◽  
Low Income Countries ◽  
Disease Dynamics ◽  
The Impact

The incidence infectious disease is inherently dynamic in time and space. Mathematical models that account for the dynamic processes that give rise to fluctuations in disease incidence are powerful tools in disease management and control. We describe the use of dynamic models for surveillance, evaluation and prediction of disease control efforts in low-income countries. Dynamic models can help to anticipate trends owing to intrinsic (e.g., herd immunity) or extrinsic (e.g., seasonality) forces that may confound efforts to isolate the impact of specific interventions. Infectious disease dynamics are frequently nonlinear, meaning that future outcomes are difficult to predict through simple extrapolation of present conditions. Thus, dynamic models can help to explore the potential consequences of proposed interventions. These projections can alert managers to the potential for unintended consequences of control and help to define effect sizes for the design of conventional studies of the impact of interventions.

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