scholarly journals Analysis of a malaria model with mosquito host choice and bed-net control

2015 ◽  
Vol 08 (06) ◽  
pp. 1550077 ◽  
Author(s):  
Bruno Buonomo
Keyword(s):  
Reproduction Number ◽  
Host Choice ◽  
Bed Nets ◽  
Bed Net ◽  
Host Manipulation ◽  
Host Preferences ◽  
Insecticide Treated Bed Nets ◽  
The Impact ◽  
Malaria Model ◽  
Disease Free

A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed-nets usage. The occurrence of a backward bifurcation at R0 = 1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic reproduction number is less than unity. This phenomenon is found to be caused by disease-induced human mortality. The global asymptotic stability of the endemic equilibrium for R0 > 1 is proved, by using the geometric method for global stability. Therefore, the disease becomes endemic for R0 > 1 regardless of the number of initial cases in both the human and vector populations. Finally, the impact on system dynamics of vector's host preferences and bed-net usage behavior is investigated.

scholarly journals A singularly perturbed vector-bias malaria model incorporating bed-net control

2021 ◽  
Author(s):  
Sanaa Salman
Keyword(s):  
Time Scale ◽  
Disease Model ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Bed Nets ◽  
Bed Net ◽  
Model Dynamics ◽  
Insecticide Treated Bed Nets ◽  
Perturbed Model ◽  
Malaria Model

A malaria transmission disease model with host selectivity and Insecticide treated bed nets (ITNs), as an intervention for controlling the disease, is formulated. Since the vector is an insect, the vector time scale is much more expeditious than the host time scale. This leads to a singularly perturbed model with two distinctive intrinsic time scales, two-slow for the host and one-fast for the vector. The basic reproduction number R0 is calculated and the local stability analysis is performed at equilibria of the model when the perturbation parameter ɛ > 0. The model is analyzed when ɛ → 0 using asymptotic expansions technique. Merging bed-net control, vector-bias, and singular perturbation have a notable effect on the model dynamics. It is shown that if over %30 of humans use ITNs, malaria disease burden can be reduced. The dynamics on the slow surface indicate that the infected vectors decays very fast when ɛ = 0.001 according to the numerical simulations.

scholarly journals Bifurcation and Sensitivity Analysis of a Malaria Model with Isolated Drug Resistant Population

2021 ◽  
Vol 24 (11) ◽  
pp. 1949-1953
Author(s):  
AO Sangotola
Keyword(s):  
Sensitivity Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Nonlinear Differential Equations ◽  
Drug Resistant ◽  
Resistant Population ◽  
The Impact ◽  
Malaria Model ◽  
Disease Free ◽  
The Basic Reproduction Number

A malaria model with isolated drug resistant population after the first line of treatment is presented using six systems of first order nonlinear differential equations. The disease free equilibrium point and the basic reproduction number are determined. Local stability of the disease free equilibrium is determined and the conditions for the existence of endemic equilibrium. Bifurcation analysis reveals the existence of backward bifurcation. Sensitivity analysis is used to determine the impact of the model parameter on the basic reproduction number. Early detection and using correct dosage will go a long way to prevent drug resistance. Keywords: Malaria, Bifurcation, Basic reproduction number, Stability, Equilibrium.

scholarly journals Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

2021 ◽  
Vol 83 (4) ◽  
Author(s):  
Mahmoud A. Ibrahim ◽  
Attila Dénes
Keyword(s):  
Zika Virus ◽  
Reproduction Number ◽  
Virus Disease ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free

AbstractWe present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number $${\mathscr {R}}_{0}$$ R 0 as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If $${\mathscr {R}}_0 < 1,$$ R 0 < 1 , then the disease-free periodic solution is globally asymptotically stable, while if $${\mathscr {R}}_0 > 1,$$ R 0 > 1 , then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

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.

scholarly journals Modeling the effect of temperature variability on malaria control strategies

2020 ◽  
Vol 15 ◽  
pp. 65
Author(s):  
Salisu M. Garba ◽  
Usman A. Danbaba
Keyword(s):  
Control Strategies ◽  
Effect Of Temperature ◽  
Bed Nets ◽  
Asymptotically Stable ◽  
Temperature Changes ◽  
Offspring Number ◽  
Local Asymptotic Stability ◽  
Reproduction Numbers ◽  
The Impact ◽  
Disease Free

In this study, a non-autonomous (temperature dependent) and autonomous (temperature independent) models for the transmission dynamics of malaria in a population are designed and rigorously analysed. The models are used to assess the impact of temperature changes on various control strategies. The autonomous model is shown to exhibit the phenomenon of backward bifurcation, where an asymptotically-stable disease-free equilibrium (DFE) co-exists with an asymptotically-stable endemic equilibrium when the associated reproduction number is less than unity. This phenomenon is shown to arise due to the presence of imperfect vaccines and disease-induced mortality rate. Threshold quantities (such as the basic offspring number, vaccination and host type reproduction numbers) and their interpretations for the models are presented. Conditions for local asymptotic stability of the disease-free solutions are computed. Sensitivity analysis using temperature data obtained from Kwazulu Natal Province of South Africa [K. Okuneye and A.B. Gumel. Mathematical Biosciences 287 (2017) 72–92] is used to assess the parameters that have the most influence on malaria transmission. The effect of various control strategies (bed nets, adulticides and vaccination) were assessed via numerical simulations.

scholarly journals Seasonality Impact on the Transmission Dynamics of Tuberculosis

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Yali Yang ◽  
Chenping Guo ◽  
Luju Liu ◽  
Tianhua Zhang ◽  
Weiping Liu
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Autonomous Systems ◽  
Positive Periodic Solution ◽  
Transmission Dynamics ◽  
Uniform Persistence ◽  
Globally Asymptotically Stable ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

The statistical data of monthly pulmonary tuberculosis (TB) incidence cases from January 2004 to December 2012 show the seasonality fluctuations in Shaanxi of China. A seasonality TB epidemic model with periodic varying contact rate, reactivation rate, and disease-induced death rate is proposed to explore the impact of seasonality on the transmission dynamics of TB. Simulations show that the basic reproduction number of time-averaged autonomous systems may underestimate or overestimate infection risks in some cases, which may be up to the value of period. The basic reproduction number of the seasonality model is appropriately given, which determines the extinction and uniform persistence of TB disease. If it is less than one, then the disease-free equilibrium is globally asymptotically stable; if it is greater than one, the system at least has a positive periodic solution and the disease will persist. Moreover, numerical simulations demonstrate these theorem results.

scholarly journals A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

2020 ◽  
Author(s):  
Kenneth Uzoma Egeonu ◽  
Simeon Chioma Inyama ◽  
Andrew Omame
Keyword(s):  
Optimal Control ◽  
Drug Resistance ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Dynamical Property ◽  
Backward Bifurcation ◽  
Infection Model ◽  
Existence Of Optimal Control ◽  
The Impact ◽  
Disease Free

A mathematical model for two strains of Malaria and Cholera with optimal control is studied and analyzed to assess the impact of treatment controls in reducing the burden of the diseases in a population, in the presence of malaria drug resistance. The model is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is proven not to exist. The necessary conditions for the existence of optimal control and the optimality system for the model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.

scholarly journals Analysis of a Malaria Transmission Model in Children

2020 ◽  
Vol 24 (5) ◽  
pp. 789-798
Author(s):  
F.Y. Eguda ◽  
A.C. Ocheme ◽  
M.M. Sule ◽  
J. Andrawus ◽  
I.B. Babura
Keyword(s):  
Malaria Transmission ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Transmission Model ◽  
Acquired Immunity ◽  
Asymptotically Stable ◽  
Threshold Parameter ◽  
Malaria Model ◽  
Disease Free

In this paper, a nine compartmental model for malaria transmission in children was developed and a threshold parameter called control reproduction number which is known to be a vital threshold quantity in controlling the spread of malaria was derived. The model has a disease free equilibrium which is locally asymptotically stable if the control reproduction number is less than one and an endemic equilibrium point which is also locally asymptotically stable if the control reproduction number is greater than one. The model undergoes a backward bifurcation which is caused by loss of acquired immunity of recovered children and the rate at which exposed children progress to the mild stage of infection. Keywords: Malaria, Model, Backward Bifurcation, Local Stability.

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