scholarly journals A Malaria Model with Two Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hui Wan ◽  
Jing-an Cui
Keyword(s):  
Basic Reproduction Number ◽  
Time Delays ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Transmission Model ◽  
Two Delays ◽  
Malaria Model ◽  
The Basic Reproduction Number

A transmission model of malaria with two delays is formulated. We calculate the basic reproduction numberR0for the model. It is shown that the basic reproduction number is a decreasing function of two time delays. The existence of the equilibria is studied. Our results suggest that the model undergoes a backward bifurcation, which implies that bringing the basic reproduction number below 1 is not enough to eradicate malaria.

A THEORETICAL ASSESSMENT OF THE EFFECTS OF DISTRIBUTED DELAY ON THE TRANSMISSION DYNAMICS OF HEPATITIS B

2015 ◽  
Vol 23 (03) ◽  
pp. 423-455
Author(s):  
P. MOUOFO TCHINDA ◽  
JEAN JULES TEWA ◽  
BOULECHARD MEWOLI ◽  
SAMUEL BOWONG
Keyword(s):  
Drug Therapy ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Time Delays ◽  
Reproduction Number ◽  
Distributed Delay ◽  
Global Dynamics ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, we investigate the global dynamics of a system of delay differential equations which describes the interaction of hepatitis B virus (HBV) with both liver and blood cells. The model has two distributed time delays describing the time needed for infection of cell and virus replication. We also include the efficiency of drug therapy in inhibiting viral production and the efficiency of drug therapy in blocking new infection. We compute the basic reproduction number and find that increasing delays will decrease the value of the basic reproduction number. We study the sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Our analysis reveals that the model exhibits the phenomenon of backward bifurcation (where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium when the basic reproduction number is less than unity). Numerical simulations are presented to evaluate the impact of time-delays on the prevalence of the disease.

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.

scholarly journals Investigating the Impact of Social Awareness and Rapid Test on A COVID-19 Transmission Model

2021 ◽  
Vol 4 (1) ◽  
pp. 46-64
Author(s):  
Muhammad Afief Balya ◽  
Bunga Oktaviani Dewi ◽  
Faza Indah Lestari ◽  
Gayatri Ratu ◽  
Hanna Rosuliyana ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Rapid Test ◽  
Social Awareness ◽  
Transmission Model ◽  
Media Campaign ◽  
Single Intervention ◽  
The Impact ◽  
The Basic Reproduction Number

In this article, we propose and analyze a mathematical model of COVID-19 transmission among a closed population, with social awareness and rapid test intervention as the control variables. For this, we have constructed the model using a compartmental system of the ordinary differential equations. Dynamical analysis regarding the existence and local stability of equilibrium points is conducted rigorously. Our analysis shows that COVID-19 will disappear from the population if the basic reproduction number is less than one, and persist if the basic reproduction number is greater than one. In addition, we have shown a trans-critical bifurcation phenomenon based on our proposed model when the basic reproduction number equals one. From the elasticity analysis, we have observed that rapid testing is more promising in reducing the basic reproduction number as compared to a media campaign to improve social awareness on COVID-19. Using the Pontryagin Maximum Principle (PMP), the characterization of our optimal control problem is derived analytically and solved numerically using the forward-backward iterative algorithm. Our cost-effectiveness analysis shows that using rapid test and media campaigns partially are the best intervention strategy to reduce the number of infected humans with the minimum cost of intervention. If the intervention is to be implemented as a single intervention, then using solely the rapid test is a more promising and low-cost option in reducing the number of infected individuals vis-a-vis a media campaign to increase social awareness as a single intervention.

scholarly journals COVID-19 disease transmission model considering direct and indirect transmission

2020 ◽  
Vol 202 ◽  
pp. 12008
Author(s):  
Dipo Aldila
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Model ◽  
Indirect Transmission ◽  
Variation Of Parameters ◽  
The Media ◽  
Disease Transmission Model ◽  
The Basic Reproduction Number

A mathematical model for understanding the COVID-19 transmission mechanism proposed in this article considering two important factors: the path of transmission (direct-indirect) and human awareness. Mathematical model constructed using a four-dimensional ordinary differential equation. We find that the Covid-19 free state is locally asymptotically stable if the basic reproduction number is less than one, and unstable otherwise. Unique endemic states occur when the basic reproduction number is larger than one. From sensitivity analysis on the basic reproduction number, we find that the media campaign succeeds in suppressing the endemicity of COVID-19. Some numerical experiments conducted to show the dynamic of our model respect to the variation of parameters value.

scholarly journals Stability Analysis and Semi-analytic Solution to a SEIR-SEI Malaria Transmission Model Using HE’s Variational Iteration Method

2020 ◽  
Author(s):  
Kingsley Timilehin Akinfe ◽  
Adedapo Chris Loyinmi
Keyword(s):  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Iteration Method ◽  
Reproduction Number ◽  
Gaussian Elimination ◽  
Equilibrium Points ◽  
Variational Iteration Method ◽  
Transmission Model ◽  
Variational Iteration ◽  
The Basic Reproduction Number

We have considered a SEIR-SEI Vector-host mathematical model which captures malaria transmission dynamics, described and built on 7-dimensional nonlinear ordinary differential equations. We compute the basic reproduction number of the model; examine the positivity and boundedness of the model compartments in a region using well established methods viz: Cauchy’s differential theorem, Birkhoff & Rota’s theorem which verifies and reveals the well-posedness, and carrying capacity of the model respectively, the existence of the Disease-Free (DFE) and Endemic (EDE) equilibrium points were determined and examined. Using the Gaussian elimination method and the Routh-hurwitz criterion, we convey stability analyses at DFE and EDE points which indicates that the DFE (malaria-free) and the EDE (epidemic outbreak) point occurs when the basic reproduction number is less than unity (one) and greater than unity (one) respectively. We obtain a solution to the model using the Variational iteration method (VIM) (an unprecedented method) to each population compartments and verify the efficacy, reliability and validity of the proposed method by comparing the respective solutions via tables and combined plots with the computer in-built Runge-kutta-Felhberg of fourth-fifths order (RKF-45). We illustrate the combined plot profiles of each compartment in the model, showing the dynamic behavior of these compartments; then we speculate that VIM is efficient and capable to conduct analysis on Malaria models and other epidemiological models.

scholarly journals Threshold Dynamics of an HIV-TB Co-infection Model with Multiple Time Delays

2021 ◽  
Vol 53 ◽  
Author(s):  
M. Pitchaimani ◽  
A. Saranya Devi
Keyword(s):  
Basic Reproduction Number ◽  
Time Delays ◽  
Reproduction Number ◽  
Numerical Study ◽  
Single Infection ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Basic Reproduction Number

In this article, a mathematical model to study the dynamics ofHIV-TB co-infection with two time delays is proposed and analyzed.We compute the basic reproduction number for each disease (HIV andTB) which acts as a threshold parameters. The disease dies out whenthe basic reproduction number of both diseases are less than unityand persists when the basic reproduction number of atleast one of thedisease is greater than unity. A numerical study on the model is alsoperformed to investigate the influence of certain key parameters on thespread of the disease. Mathematical analysis of our model shows thatswitching co-infection (HIV and TB) to single infection (HIV) can beachieved by imposing treatment for both the disease simultaneouslyas TB eradication is made possible with effective treatment.

scholarly journals Analisis dinamik model SVEIR pada penyebaran penyakit campak

2020 ◽  
Vol 1 (2) ◽  
pp. 57-64
Author(s):  
Sitty Oriza Sativa Putri Ahaya ◽  
Emli Rahmi ◽  
Nurwan Nurwan
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Total Population ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Model ◽  
Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this article, we analyze the dynamics of measles transmission model with vaccination via an SVEIR epidemic model. The total population is divided into five compartments, namely the Susceptible, Vaccinated, Exposed, Infected, and Recovered populations. Firstly, we determine the equilibrium points and their local asymptotically stability properties presented by the basic reproduction number R0. It is found that the disease free equilibrium point is locally asymptotically stable if satisfies R01 and the endemic equilibrium point is locally asymptotically stable when R01. We also show the existence of forward bifurcation driven by some parameters that influence the basic reproduction number R0 i.e., the infection rate α or proportion of vaccinated individuals θ. Lastly, some numerical simulations are performed to support our analytical results.

DYNAMICAL MODEL OF VIVAX MALARIA INTERMITTENCE ATTACK IN VIVO

2009 ◽  
Vol 02 (04) ◽  
pp. 507-524 ◽  
Author(s):  
ZHIJUN DONG ◽  
JING-AN CUI
Keyword(s):  
Numerical Simulations ◽  
Plasmodium Vivax ◽  
Human Body ◽  
Basic Reproduction Number ◽  
Vivax Malaria ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Malaria Model ◽  
The Basic Reproduction Number

Dynamical behavior of a vivax malaria model is provided and regular recurrences of the symptoms of the tertian fever are described in the human body. We calculate the basic reproduction number R0 and explain the connection between the basic reproduction number and the parasite-threshold. If R0 < 1, then plasmodium vivax will be eliminated. If R0 > 1, then malarial parasites are survivable and there is a so called parasite-threshold. When the value of the parasites is larger than this parasite-threshold the symptoms of the tertian fever appear; otherwise, if the value of the parasites is less than this parasite-threshold the tertian fever cannot give signs of the symptoms suddenly in vivo. We illustrate that the gravity of infected baby is worse than that of infected grownup and also explain that the advancing of the vivax malaria can be arrested by eliminating malarial parasites in erythrocyte stage with clinical treatment by numerical simulations.

Global dynamics for a TB transmission model with age-structure and delay

2020 ◽  
Vol 13 (07) ◽  
pp. 2050055
Author(s):  
Dongxue Yan ◽  
Hui Cao ◽  
Suxia Zhang
Keyword(s):  
Explicit Formula ◽  
Global Attractor ◽  
Age Structure ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Model ◽  
Global Dynamics ◽  
Numerical Examples ◽  
Stability And Instability ◽  
The Basic Reproduction Number

This paper deals with the global dynamics of a tuberculosis (TB) model with age-structure and delay. We perform some rigorous analyses for the model, including presenting an explicit formula for the basic reproduction number of the model, addressing the persistence of the solution semi-flow and the existence of the global attractor. Based on these analyses, we establish some results on stability and instability of equilibrium of the system. Finally, some numerical examples are provided to illustrate our obtained results.

scholarly journals A Periodic West Nile Virus Transmission Model with Stage-Structured Host Population

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Junli Liu ◽  
Tailei Zhang ◽  
Qiaoling Chen
Keyword(s):  
Periodic Solution ◽  
West Nile Virus ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Model ◽  
Avian Host ◽  
West Nile ◽  
West Nile Virus Transmission ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we study an avian (host) stage-structured West Nile virus model, which incorporates seasonality as well as stage-specific mosquito biting rates. We first introduce the basic reproduction number R0 for this model and then show that the disease-free periodic solution is globally asymptotically stable when R0<1, while there exists at least one positive periodic solution and that the disease is uniformly persistent if R0>1. In the case where all coefficients are constants, for a special case, we obtain the global stability of the disease-free equilibrium, the uniqueness of the endemic equilibrium, and the permanence of the disease in terms of the basic reproduction number R0. Numerical simulations are carried out to verify the analytic result. Some sensitivity analysis of R0 is performed. Our finding shows that an increase in juvenile exposure will lead to more severe transmission. Moreover, we find that the ignorance of the seasonality may result in underestimation of the basic reproduction number R0.

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