scholarly journals Analysis of Cholera Epidemic Controlling Using Mathematical Modeling

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Kinfe Hailemariam Hntsa ◽  
Berhe Nerea Kahsay
Keyword(s):  
Mathematical Modeling ◽  
Preventive Measures ◽  
Reproduction Number ◽  
Preventive Measure ◽  
Transmission Dynamics ◽  
Cholera Epidemic ◽  
Sensitivity Indices ◽  
Existence And Stability ◽  
Theoretical Results ◽  
The Basic Reproduction Number

The purpose of this study is to see whether it is possible to eradicate the disease theoretically using mathematical modeling with the aid of numerical simulation when disease occurs in a population by implementing adequate preventive measures. For this, we consider a mathematical model for the transmission dynamics of cholera and its preventive measure as one cohort of individuals, namely, a protected cohort in addition to susceptible, infected, and recovered cohorts of individuals including the concentration of Vibrio cholerae in the contaminated aquatic reservoir with small modifications. We calculate the basic reproduction number, ℛ0, and investigate the existence and stability of equilibria. The model possessed forward bifurcation. Moreover, we compute the sensitivity indices of each parameter in relating to ℛ0 of the model. Numerical simulations are carried out to validate our theoretical results. The result indicates that the disease dies out in areas with adequate preventive measures and widespread and kills more people in areas with the inadequate preventive measures.

scholarly journals Dynamics Analysis of Avian Influenza A(H7N9) Epidemic Model

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Yun Li ◽  
Peng Qin ◽  
Juping Zhang
Keyword(s):  
Mathematical Model ◽  
Avian Influenza ◽  
Influenza A ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Dynamics Analysis ◽  
H7n9 Virus ◽  
Next Generation Matrix ◽  
Theoretical Results ◽  
The Basic Reproduction Number

The avian influenza A(H7N9) virus has certain fatal effects on human. In this paper, a mathematical model describing the transmission dynamics of avian influenza A(H7N9) between human and poultry is investigated. The basic reproduction number of the model is obtained by applying the method of the next generation matrix. Then the local and global stability of the equilibria are proven. At last, we use numerical simulations to verify the theoretical results.

scholarly journals An Age-Structured Model for Transmission Dynamics of Malaria with Infected Immigrants and Asymptomatic Carriers

2021 ◽  
Vol 47 (3) ◽  
pp. 953-968
Author(s):  
Asha S Kalula ◽  
Eunice Mureithi ◽  
Theresia Marijani ◽  
Isambi Mbalawata
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Asymptomatic Carrier ◽  
Transmission Dynamics ◽  
Asymptomatic Carriers ◽  
Sensitivity Indices ◽  
Biting Rate ◽  
Age Structured ◽  
Disease Free ◽  
The Basic Reproduction Number

An age-structured (children and adults) model for the transmission dynamics of malaria with asymptomatic carriers and infected immigrants has been analyzed. We first analyze a model without infected immigrants. It shows that the disease-free equilibrium exists and is stable when and unstable for . Also, we compute the sensitivity indices of the basic reproduction number. The basic reproduction number is most sensitive to the mosquito biting rate. Besides, the sensitivity of the basic reproduction number shows that the children's class parameters are more sensitive than those of adults. In the presence of infected immigrants, the model does not admit a disease-free equilibrium. The sensitivity of endemic equilibrium shows that the asymptomatic carrier parameters are more critical than that of infected immigrants. Also, the inflow of infectious immigrants is sensitive than that of infected immigrants. The results obtained indicate that strategies that target asymptomatic carriers and infected immigrants can help control malaria. Keywords: Age-structure; malaria; immigrants; asymptomatic carrier; nonlinear ODE model

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2106147
Author(s):  
Debkumar Pal ◽  
D Ghosh ◽  
P K Santra ◽  
G S Mahapatra
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Treatment Control ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
The Cost ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

scholarly journals Estimasi Reproduction Number Model Matematika Penyebaran Malaria di Sumba Tengah, Indonesia

2021 ◽  
Vol 2 (1) ◽  
pp. 13-19
Author(s):  
Ervin Mawo Banni ◽  
Maria A Kleden ◽  
Maria Lobo ◽  
Meksianis Zadrak Ndii
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Health Center ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Awareness Program ◽  
Awareness Programs ◽  
Malaria Eradication

Malaria is transmitted via a bite of mosquitoes and it is dangerous if it is not properly treated. Mathematical modeling can be formulated to understand the disease transmission dynamics. In this paper, a mathematical model with an awareness program has been formulated and the reproduction number has been estimated against the data from Weeluri Health Center, Mamboro District, Central Sumba. The calculation showed that the reproduction number is R0 = 1.2562. Results showed that if the efficacy of the awareness program is lower than 20%, the reproduction number is still above unity. If the efficacy of the awareness program is higher than 20%, the reproduction number is lower than unity. This implies that the efficacy of awareness programs is the key to the success of Malaria eradication.

scholarly journals Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students

2020 ◽  
Vol 16 (32) ◽  
pp. 195-223
Author(s):  
Edgardo Pérez
Keyword(s):  
Mathematical Modeling ◽  
College Students ◽  
Mathematical Model ◽  
Drinking Behavior ◽  
Preventive Measure ◽  
Nonlinear Mathematical Model ◽  
Consumption Behavior ◽  
Existence And Stability ◽  
Drugs And Crime ◽  
The Impact

In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.

scholarly journals Analysis of a diffusive cholera model incorporating latency and bacterial hyperinfectivity

2021 ◽  
Vol 20 (11) ◽  
pp. 3921
Author(s):  
Wei Yang ◽  
Jinliang Wang
Keyword(s):  
Lyapunov Functional ◽  
Global Attractivity ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Flux Boundary Condition ◽  
Nonlocal Reaction ◽  
Theoretical Results ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>In this paper, we are concerned with the threshold dynamics of a diffusive cholera model incorporating latency and bacterial hyperinfectivity. Our model takes the form of spatially nonlocal reaction-diffusion system associated with zero-flux boundary condition and time delay. By studying the associated eigenvalue problem, we establish the threshold dynamics that determines whether or not cholera will spread. We also confirm that the threshold dynamics can be determined by the basic reproduction number. By constructing Lyapunov functional, we address the global attractivity of the unique positive equilibrium whenever it exists. The theoretical results are still hold for the case when the constant parameters are replaced by strictly positive and spatial dependent functions.</p>

scholarly journals Analysis of the Mathematical Model for the Spread of Pine Wilt Disease

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiangyun Shi ◽  
Guohua Song
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Endemic Equilibrium ◽  
Feasible Region ◽  
Global Dynamics ◽  
Pine Wilt ◽  
Theoretical Results ◽  
The Basic Reproduction Number

This paper formulates and analyzes a pine wilt disease model. Mathematical analyses of the model with regard to invariance of nonnegativity, boundedness of the solutions, existence of nonnegative equilibria, permanence, and global stability are presented. It is proved that the global dynamics are determined by the basic reproduction numberℛ0and the other valueℛcwhich is larger thanℛ0. Ifℛ0andℛcare both less than one, the disease-free equilibrium is asymptotically stable and the pine wilt disease always dies out. If one is between the two values, though the pine wilt disease could occur, the outbreak will stop. If the basic reproduction number is greater than one, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists. Numerical simulations are carried out to illustrate the theoretical results, and some disease control measures are especially presented by these theoretical results.

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.

DYNAMICS OF A MODEL FOR VIRULENT PHAGE T4

2008 ◽  
Vol 16 (04) ◽  
pp. 597-611 ◽  
Author(s):  
ZHIPENG QIU
Keyword(s):  
Population Density ◽  
Reproduction Number ◽  
Bacteriophage T4 ◽  
Sufficient Conditions ◽  
Chemostat Model ◽  
Virulent Phage ◽  
E Coli ◽  
Phage T4 ◽  
Theoretical Results ◽  
The Basic Reproduction Number

In this paper, the asymptotical behavior of a chemostat model for E. coli and the virulent phage T4 is analyzed. The basic reproduction number R0 is proved to be a threshold which determines the outcome of the virulent phage T4. If R0 < 1, the virus dies out; if R0 > 1, the virus persists. Sufficient conditions for the Hopf bifurcation are also established. The theoretical results show that increasing the input of nutrient will result in an increase in the equilibrium population density of the virulent bacteriophage T4, but will have no effect on the equilibrium population density of E. coli. The results also show that increasing the input of nutrient or increasing the average lytic time for the infected E. coli can destabilize the interaction between E. coli and T4.

Sign in / Sign up

Export Citation Format

Share Document