A 2-DIMENSIONAL MODEL FOR MACROPARASITIC INFECTIONS IN A HOST WITH LOGISTIC GROWTH

1995 ◽  
Vol 03 (03) ◽  
pp. 833-849 ◽  
Author(s):  
ANDREA PUGLIESE ◽  
ROBERTO ROSÀ
Keyword(s):  
Carrying Capacity ◽  
Negative Binomial ◽  
Host Population ◽  
Specific Pattern ◽  
Logistic Growth ◽  
Contact Rate ◽  
Dimensional Model ◽  
Parasite Distribution ◽  
Stable Equilibria ◽  
Disease Free

We analysed a model for the interaction of a macroparasite and a host population growing logistically. The model is obtained by approximating the parasite distribution with a negative binomial with a fixed clumping parameter. By letting the contact rate k vary, we found a complex pattern of bifurcations, including subcritical bifurcations of the disease-free equilibrium, Hopf and homoclinic bifurcations. The specific pattern depends on the interaction of the various parameters; in particular, alternative stable equilibria may occur only when the carrying capacity KN is sufficiently large, while periodic solutions may occur for all values of KN, if k is large enough.

scholarly journals Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jianping Wang ◽  
Shujing Gao ◽  
Yueli Luo ◽  
Dehui Xie
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.

The dynamics of a delayed deterministic and stochastic epidemic SIR models with a saturated incidence rate

2018 ◽  
Vol 26 (4) ◽  
pp. 235-245 ◽  
Author(s):  
Modeste N’zi ◽  
Ilimidi Yattara
Keyword(s):  
Stochastic Model ◽  
White Noise ◽  
Incidence Rate ◽  
Deterministic Model ◽  
Contact Rate ◽  
Almost Sure Stability ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Global Positive Solution ◽  
Disease Free

AbstractWe treat a delayed SIR (susceptible, infected, recovered) epidemic model with a saturated incidence rate and its perturbation through the contact rate using a white noise. We start with a deterministic model and then add a perturbation on the contact rate using a white noise to obtain a stochastic model. We prove the existence and uniqueness of the global positive solution for both deterministic and stochastic delayed differential equations. Under suitable conditions on the parameters, we study the global asymptotic stability of the disease-free equilibrium of the deterministic model and the almost sure stability of the disease-free equilibrium of the stochastic model.

scholarly journals Simulating the next steps in badger control for bovine tuberculosis in England

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248426
Author(s):  
Graham C. Smith ◽  
Richard Budgey
Keyword(s):  
Simulation Model ◽  
Carrying Capacity ◽  
Bovine Tuberculosis ◽  
Management Strategies ◽  
Fertility Control ◽  
Host Population ◽  
Dramatic Reduction ◽  
Control Option ◽  
Badger Vaccination ◽  
The Uk

Industry-led culling of badgers has occurred in England to reduce the incidence of bovine tuberculosis in cattle for a number of years. Badger vaccination is also possible, and a move away from culling was “highly desirable” in a recent report to the UK government. Here we used an established simulation model to examine badger control option in a post-cull environment in England. These options included no control, various intermittent culling, badger vaccination and use of a vaccine combined with fertility control. The initial simulated cull led to a dramatic reduction in the number of infected badgers present, which increased slowly if there was no further badger management. All three approaches led to a further reduction in the number of infected badgers, with little to choose between the strategies. We do note that of the management strategies only vaccination on its own leads to a recovery of the badger population, but also an increase in the number of badgers that need to be vaccinated. We conclude that vaccination post-cull, appears to be particularly effective, compared to vaccination when the host population is at carrying capacity.

scholarly journals Determination of the Equilibrium Point According to a Temporal Model of Rehydration in a Population with Cholera in Logistic Growth

2020 ◽  
pp. 1-5
Author(s):  
K. O. Jackob
Keyword(s):  
Equilibrium Point ◽  
Medical Attention ◽  
Logistic Growth ◽  
Cholera Outbreak ◽  
Temporal Model ◽  
Multiple Interaction ◽  
Transmission Pathways ◽  
Untreated Individuals ◽  
Disease Free

Cholera is an infection of the small intestine of humans caused by a gram-negative bacterium called Vibrio cholerae. It is spread through eating food or drinking water contaminated with faeces from an infected person. It causes rapid dehydration and general body imbalance, and can lead to death since untreated individuals suer severely from diarrhea and vomiting. Its dynamics involves multiple interaction between the human host, the pathogen and the environment which contributes to both human to human and indirect environment to human transmission pathways. Rehydration is critical in reducing cholera death. This has been studied by other scholars but they did not consider delay in rehydration on the spread of cholera. In this paper, I formulate a mathematical model based on system of ordinary differential equation with rehydration on the spread of cholera in a logistically growing population. The existence of the steady states and the basic reproduction number is established such that disease free equilibrium point exists. Determination of endemic equilibrium shows that the model has positive points. The findings will be signicant in the sense that timely rehydration should be done during cholera outbreak and will enable individuals with symptoms to seek immediate medical attention.

scholarly journals Psi-Caputo Logistic Population Growth Model

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muath Awadalla ◽  
Yves Yannick Yameni Noupoue ◽  
Kinda Abu Asbeh
Keyword(s):  
Population Growth ◽  
Fractional Derivative ◽  
Carrying Capacity ◽  
Chinese Population ◽  
Logistic Model ◽  
Logistic Equation ◽  
Logistic Growth ◽  
Growth Equation ◽  
Uniqueness Of The Solution ◽  
Better Than

This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α  = 1.6455.

scholarly journals Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Caijuan Yan ◽  
Jianwen Jia
Keyword(s):  
Hopf Bifurcation ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Sir Epidemic Model ◽  
Medical Resources ◽  
Reproduction Ratio ◽  
Disease Free ◽  
Information Variable

We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratioℛ0<1, we discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov functional. Ifℛ0>1, we obtain sufficient conditions under which the endemic equilibriumE*of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions.

scholarly journals Heterogeneity in transmission parameters of hookworm infection within the baseline data from the TUMIKIA study in Kenya

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
James E. Truscott ◽  
Alison K. Ower ◽  
Marleen Werkman ◽  
Katherine Halliday ◽  
William E. Oswald ◽  
...  
Keyword(s):  
Negative Binomial ◽  
Positive Association ◽  
Monitoring And Evaluation ◽  
Host Population ◽  
Transmission Model ◽  
High Coverage ◽  
Study Region ◽  
Transmission Parameters ◽  
Parasite Aggregation ◽  
The Impact

Abstract Background As many countries with endemic soil-transmitted helminth (STH) burdens achieve high coverage levels of mass drug administration (MDA) to treat school-aged and pre-school-aged children, understanding the detailed effects of MDA on the epidemiology of STH infections is desirable in formulating future policies for morbidity and/or transmission control. Prevalence and mean intensity of infection are characterized by heterogeneity across a region, leading to uncertainty in the impact of MDA strategies. In this paper, we analyze this heterogeneity in terms of factors that govern the transmission dynamics of the parasite in the host population. Results Using data from the TUMIKIA study in Kenya (cluster STH prevalence range at baseline: 0–63%), we estimated these parameters and their variability across 120 population clusters in the study region, using a simple parasite transmission model and Gibbs-sampling Monte Carlo Markov chain techniques. We observed great heterogeneity in R0 values, with estimates ranging from 1.23 to 3.27, while k-values (which vary inversely with the degree of parasite aggregation within the human host population) range from 0.007 to 0.29 in a positive association with increasing prevalence. The main finding of this study is the increasing trend for greater parasite aggregation as prevalence declines to low levels, reflected in the low values of the negative binomial parameter k in clusters with low hookworm prevalence. Localized climatic and socioeconomic factors are investigated as potential drivers of these observed epidemiological patterns. Conclusions Our results show that lower prevalence is associated with higher degrees of aggregation and hence prevalence alone is not a good indicator of transmission intensity. As a consequence, approaches to MDA and monitoring and evaluation of community infection status may need to be adapted as transmission elimination is aimed for by targeted treatment approaches.

scholarly journals Carrying Capacity of a Population Diffusing in a Heterogeneous Environment

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 49 ◽  
Author(s):  
D.L. DeAngelis ◽  
Bo Zhang ◽  
Wei-Ming Ni ◽  
Yuanshi Wang
Keyword(s):  
Population Size ◽  
Carrying Capacity ◽  
Heterogeneous System ◽  
Total Population ◽  
Reaction Diffusion ◽  
Maximum Growth ◽  
Reaction Diffusion Equations ◽  
Logistic Growth ◽  
Chemostat Model ◽  
Total Population Size

The carrying capacity of the environment for a population is one of the key concepts in ecology and it is incorporated in the growth term of reaction-diffusion equations describing populations in space. Analysis of reaction-diffusion models of populations in heterogeneous space have shown that, when the maximum growth rate and carrying capacity in a logistic growth function vary in space, conditions exist for which the total population size at equilibrium (i) exceeds the total population that which would occur in the absence of diffusion and (ii) exceeds that which would occur if the system were homogeneous and the total carrying capacity, computed as the integral over the local carrying capacities, was the same in the heterogeneous and homogeneous cases. We review here work over the past few years that has explained these apparently counter-intuitive results in terms of the way input of energy or another limiting resource (e.g., a nutrient) varies across the system. We report on both mathematical analysis and laboratory experiments confirming that total population size in a heterogeneous system with diffusion can exceed that in the system without diffusion. We further report, however, that when the resource of the population in question is explicitly modeled as a coupled variable, as in a reaction-diffusion chemostat model rather than a model with logistic growth, the total population in the heterogeneous system with diffusion cannot exceed the total population size in the corresponding homogeneous system in which the total carrying capacities are the same.

scholarly journals Optimal intervention strategies of staged progression HIV infections through an age-structured model with probabilities of ART drop out

2021 ◽  
Author(s):  
Ramsès Djidjou-Demasse
Keyword(s):  
Global Analysis ◽  
Hiv Infections ◽  
Host Population ◽  
Drop Out ◽  
Globally Asymptotically Stable ◽  
Optimal Intervention ◽  
Age Structured ◽  
Age Structured Model ◽  
The Impact ◽  
Disease Free

In this paper, we construct a model to describe the transmission of HIV in a homogeneous host population. By considering the specific mechanism of HIV, we derive a model structured in three successive stages: (i) primary infection, (ii) long phase of latency without symptoms and (iii) AIDS. Each HIV stage is stratified by the duration for which individuals have been in the stage, leading to a continuous age-structure model. In the first part of the paper, we provide a global analysis of the model depending upon the basic reproduction number R0. When R0<=1, then the disease-free equilibrium is globally asymptotically stable and the infection is cleared in the host population. On the contrary, if R0>1, we prove the epidemic's persistence with the asymptotic stability of the endemic equilibrium. By performing the sensitivity analysis, we then determine the impact of control-related parameters of the outbreak severity. For the second part, the initial model is extended with intervention methods. By taking into account ART interventions and the probability of treatment drop out, we discuss optimal interventions methods which minimize the number of AIDS cases.

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