Impact of fear on a delayed eco-epidemiological model for migratory birds

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Caihong Song ◽  
Ning Li
Keyword(s):  
Disease Transmission ◽  
Migratory Birds ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Model System ◽  
Epidemiological Model ◽  
Predator Population ◽  
Type Ii ◽  
Fear Effect ◽  
Simulation Results

Abstract In this paper, a delayed eco-epidemiological model including susceptible migratory birds, infected migratory birds and predator population is proposed by us. The interaction between predator and prey is represented by functional response of Leslie–Gower Holling-type II. Fear effect is considered in the model. We assume that the growth rate and activity of prey population can be reduced because of fear effect of predator, and this series of behaviors will indirectly slow down the spread of diseases. Positivity, boundedness, persistence criterion, and stability of equilibrium points of the system are analyzed. Transcritical bifurcation and Hopf-bifurcation respect to important parameters of the system have been discussed both analytically and numerically (e.g. fear of predator, disease transmission rate of prey, and delay). Numerical simulation results show that fear can not only eliminate the oscillation behavior caused by high disease transmission rate and long delay in the model system, but also eliminate the disease.

scholarly journals Analisis Kestabilan Model Predator-Prey dengan Adanya Faktor Tempat Persembunyian Menggunakan Fungsi Respon Holling Tipe III

2021 ◽  
Vol 3 (2) ◽  
pp. 88
Author(s):  
Riris Nur Patria Putri ◽  
Windarto Windarto ◽  
Cicik Alfiniyah
Keyword(s):  
Numerical Simulation ◽  
Response Function ◽  
Equilibrium Points ◽  
Prey Population ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Asymptotic Stable ◽  
Simulation Results ◽  
Model Predator

Predation is interaction between predator and prey, where predator preys prey. So predators can grow, develop, and reproduce. In order for prey to avoid predators, then prey needs a refuge. In this thesis, a predator-prey model with refuge factor using Holling type III response function which has three populations, i.e. prey population in the refuge, prey population outside the refuge, and predator population. From the model, three equilibrium points were obtained, those are extinction of the three populations which is unstable, while extinction of predator population and coexistence are asymptotic stable under certain conditions. The numerical simulation results show that refuge have an impact the survival of the prey.

scholarly journals Dynamics of an Epidemic Model under the Influence of Environmental Stress

2021 ◽  
Vol 16 (2) ◽  
pp. 201-243
Author(s):  
Sangeeta Saha ◽  
Guruprasad Samanta
Keyword(s):  
Environmental Stress ◽  
Environmental Pollution ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Dynamical Behaviour ◽  
Treatment Policy ◽  
The Stability ◽  
The Cost ◽  
The Impact

We have considered a compartmental epidemiological model with infectious disease to observe the influence of environmental stress on disease transmission. The proposed model is well-defined as the population at each compartment remains positive and bounded with time. Dynamical behaviour of the model is observed by the stability and bifurcation analysis at the equilibrium points. Also, numerical simulation supports the theoretical proofs and the result shows that the system undergoes a forward bifurcation around the disease-free equilibrium. Our results indicate that with the increase of environmental pollution, the overall infected population increases. Also, the disease transmission rate among the susceptible and stressed population from asymptomatically infected individuals plays a crucial role to make a system endemic. A corresponding optimal control problem has also been proposed to control the disease prevalence as well as to minimize the cost by choosing the vaccination policy before being infected and treatment policy to the infected as control variables. Numerical figures indicate that the vaccination provided to susceptible needs some time to reduce the disease transmission but the vaccination provided to stressed individuals works immediately after implementation. The treatment policy for symptomatically infected individuals works with a higher rate at an earlier stage but the intensity decreases with time. Simultaneous implementation of all control interventions is more useful to reduce the size of overall infective individuals and also to minimize the economic burden. Hence, this research clearly expresses the impact of environmental pollution (specifically the influence of environmental stress) on the disease transmission in the population.

scholarly journals A realistic model for the periodic dynamics of the hand-foot-and-mouth disease

2021 ◽  
Vol 7 (2) ◽  
pp. 2585-2601
Author(s):  
I. A. Moneim ◽  
◽  
G. A. Mosa
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Foot And Mouth Disease ◽  
Vaccination Strategy ◽  
Mouth Disease ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Good Prediction ◽  
Foot And Mouth ◽  
Simulation Results

<abstract><p>In this paper, an SEIQRS model with a periodic vaccination strategy is studied for the dynamics of the Hand-Foot-and-Mouth Disease (HFMD). This model incorporates a seasonal variation in the disease transmission rate $ \beta (t) $. Our model has a unique disease free periodic solution (DFPS). The basic reproductive number $ R_{0} $ and its lower and upper bounds, $ R_{0}^{inf} $ and $ R_{0}^{sup} $ respectively, are defined. We show that the DFPS is globally asymptotically stable when $ R_{0}^{sup} &lt; 1 $ and unstable if $ R_{0}^{inf} &gt; 1 $. Computer simulations of our model have been conducted using a novel periodic function of the contact rate. This novel function imitates the seasonality in the observed, multi-peaks pattern, data. Clear and good matching between real data and the obtained simulation results are shown. The obtained simulation results give a good prediction and possible control of the disease dynamics.</p></abstract>

scholarly journals Density Dependent Predator Death Prevalence Chaos in a Tri-trophic Food Chain Model

2008 ◽  
Vol 13 (3) ◽  
pp. 305-324 ◽  
Author(s):  
M. Bandyopadhyay ◽  
S. Chatterjee ◽  
S. Chakraborty ◽  
J. Chattopadhyay
Keyword(s):  
Food Chain ◽  
Death Rate ◽  
Chaotic Dynamics ◽  
Equilibrium Points ◽  
Model System ◽  
Chain Model ◽  
Predator Population ◽  
Predator Species ◽  
Density Dependent ◽  
Food Chain Model

Ecological systems have all the properties to produce chaotic dynamics. To predict the chaotic behavior in an ecological system and its possible control mechanism is interesting. Aziz-Alaoui [1] considered a tri-trophic food-chain model with modified Leslie-Gower type growth rate for top-predator population and established the chaotic dynamics exhibited by the model system for a certain choice of parameter values. We have modified the said model by incorporating density dependent death rate for predator population. Our mathematical findings reveal the fact that there are two coexisting equilibrium points one of which is a source and the other one is a sink. The positive equilibrium point which is sink is actually globally asymptotically stable under certain parametric conditions. Numerical experiment analysis shows that the model system are capable to produce chaotic dynamics when the rate of intra specific completion is very low and chaotic dynamics disappears for a certain value of the rate of intra specific completion for predator species. Our results suggest that the consideration of density dependent death rate for predator species have the ability to control the chaotic dynamics.

scholarly journals The Dynamics of an Eco-Epidemiological Model with Allee Effect and Harvesting in the Predator

2020 ◽  
Vol 55 (2) ◽  
Author(s):  
Huda Abdul Satar
Keyword(s):  
Allee Effect ◽  
Equilibrium Points ◽  
Epidemiological Model ◽  
Global Dynamics ◽  
Local Bifurcation ◽  
Type Ii ◽  
Safe Area ◽  
Nonlinear Harvesting ◽  
Disease In Prey ◽  
Type Ii Functional Response

The aim of this study was to propose and evaluate an eco-epidemiological model with Allee effect and nonlinear harvesting in predators. It was assumed that there is an SI-type of disease in prey, and only portion of the prey would be attacked by the predator due to the fleeing of the remainder of the prey to a safe area. It was also assumed that the predator consumed the prey according to modified Holling type-II functional response. All possible equilibrium points were determined, and the local and global stabilities were investigated. The possibility of occurrence of local bifurcation was also studied. Numerical simulation was used to further evaluate the global dynamics and the effects of varying parameters on the asymptotic behavior of the system.

Analysis of a predator–prey model with herd behavior and disease in prey incorporating prey refuge

2019 ◽  
Vol 12 (01) ◽  
pp. 1950007 ◽  
Author(s):  
Sangeeta Saha ◽  
G. P. Samanta
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Herd Behavior ◽  
Prey Refuge ◽  
Free System ◽  
Susceptible Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Disease Free

In this work, we have introduced an eco-epidemiological model of an infected predator–prey system. Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption. Moreover, to make the model more realistic to the environment, we have introduced strong Allee effect in the susceptible population. Boundedness and positivity of the solution have been established. Local stability conditions of the equilibrium points have been found with the help of Routh–Hurwitz criterion and it has been observed that if a prey population is infected with a lethal disease, then both the prey (susceptible and infected) and predator cannot survive simultaneously in the system for any parametric values. The disease transmission rate and the attack rate on the susceptible have an important role to control the system dynamics. For different values of these two key parameters, we have got only healthy or disease-free or predation-free or a fluctuating disease-free or even a fluctuating predator-free system with some certain parametric conditions.

scholarly journals Dynamical analysis of a fractional order model incorporating fear in the disease transmission rate of COVID-19

2020 ◽  
Vol 99 (99) ◽  
pp. 1-17
Author(s):  
Debasis Mukherjee Debasis Mukherjee ◽  
Chandan Maji
Keyword(s):  
Fractional Order ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Three Dimensional ◽  
Dynamical Analysis ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Fear Effect ◽  
And Control ◽  
Disease Free

This paper deals with a fractional-order three-dimensional compartmental model with fear effect. We have investigated whether fear can play an important role or not to spread and control the infectious diseases like COVID-19, SARS etc. in a bounded region. The basic results on uniqueness, non-negativity and boundedness of the solution of the system are investigated. Stability analysis ensures that the disease-free equilibrium point is locally asymptotically stable if carrying capacity greater than a certain threshold value.We have also derived the conditions for which endemic equilibrium is globally asymptotically stable that means the disease persists in the system. Numerical simulation suggests that the fear factor is an important role which is observed through Hopf-bifurcation.

scholarly journals Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Xi Huo ◽  
Jing Chen ◽  
Shigui Ruan
Keyword(s):  
Disease Transmission ◽  
Large Scale ◽  
Transmission Rate ◽  
Control Strategies ◽  
Herd Immunity ◽  
Antibody Prevalence ◽  
Screening Process ◽  
Vaccination Programs ◽  
Prevalence Level ◽  
The Impact

Abstract Background The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. Methods By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. Results We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. Conclusions We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

scholarly journals The effect of social distancing on the reach of an epidemic in social networks

2021 ◽  
Author(s):  
Gregory Gutin ◽  
Tomohiro Hirano ◽  
Sung-Ha Hwang ◽  
Philip R. Neary ◽  
Alexis Akira Toda
Keyword(s):  
Public Health ◽  
Infectious Disease ◽  
Social Networks ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Disease Transmission ◽  
Global Level ◽  
Social Distancing ◽  
The Public ◽  
Simulation Results

AbstractHow does social distancing affect the reach of an epidemic in social networks? We present Monte Carlo simulation results of a susceptible–infected–removed with social distancing model. The key feature of the model is that individuals are limited in the number of acquaintances that they can interact with, thereby constraining disease transmission to an infectious subnetwork of the original social network. While increased social distancing typically reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the network, indicating the need for policies that are network dependent. Our results also reveal the importance of coordinating policies at the ‘global’ level. In particular, the public health benefits from social distancing to a group (e.g. a country) may be completely undone if that group maintains connections with outside groups that are not following suit.

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

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