MATHEMATICAL MODELLING AND ANALYSIS OF CHOLERA DISEASE DYNAMICS WITH CONTROL

A deterministic mathematical model of cholera infection incorporating health education campaign, vaccination of susceptible humans, treatment of infected human and water sanitation is developed. It is shown that the solution of the model uniquely exist, it is positive and bounded in a certain region. The disease-free equilibrium (DFE) state of the model was determined and used to compute the basic reproduction number as a threshold for effective disease management. The result from stability analysis for the disease-free equilibrium state (DFEs) shows that it is locally as well as globally asymptotically stable whenever the basic reproduction number is less than unity (). The results obtained from the sensitivity index of show that the control parameters of public health education campaign, vaccination of susceptible individuals, treatment of infected humans and water sanitation are crucial parameters to cholera management. Numerical simulations show that, expanded and improved vaccination among other interventions is crucial in decreasing cholera burden. Furthermore, from the numerical simulations and results it is recommended that a combination of mass and consistent public health education campaigns, expanded vaccination coverage, prompt treatment of infected individuals, with water sanitation, is vital to public health strategies in eradicating cholera infection and deaths in the shortest possible time

Download Full-text

The Role of Non-pharmacological Interventions on the Dynamics of Schistosomiasis

Journal of Mathematical and Fundamental Sciences ◽

10.5614/j.math.fund.sci.2021.53.2.6 ◽

2021 ◽

Vol 53 (2) ◽

pp. 243-260

Author(s):

Agatha Abokwara ◽

Chinwendu Emilian Madubueze

Keyword(s):

Public Health ◽

Health Education ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Public Health Education ◽

Control Measures ◽

Snail Control ◽

The Impact ◽

Disease Free ◽

The Basic Reproduction Number

Schistosomiasis is a neglected tropical disease affecting communities surrounded by water bodies where fishing activities take place or people go to swim, wash and cultivate crops. It poses a great risk to the health and economic life of inhabitants of the area. This study was carried out to evaluate the impact of public health education and snail control measures on the incidence of schistosomiasis. A model was developed with attention given to the snail and human populations that are the hosts of the cercariae and miracidia respectively. The existence and stability of disease-free and endemic equilibrium states were established. The disease-free and endemic equilibrium states were shown to be locally asymptotically stable whenever the basic reproduction number was less than unity. Numerical simulations of the model were carried out to evaluate the impact of interventions (public health education and snail control measures) on schistosomiasis transmission. It was observed that the implementation of low coverage snail control with highly efficacious molluscicide and massive public health education will make the basic reproduction number smaller than unity, which implies the eradication of schistosomiasis in the population.

Download Full-text

Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

Jambura Journal of Biomathematics (JJBM) ◽

10.34312/jjbm.v2i2.10483 ◽

2021 ◽

Vol 2 (2) ◽

pp. 68-79

Author(s):

Muhammad Manaqib ◽

Irma Fauziah ◽

Eti Hartati

Keyword(s):

Numerical Simulations ◽

Equilibrium Point ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Endemic Equilibrium ◽

Reproduction Numbers ◽

Geometric Picture ◽

Disease Free ◽

The Basic Reproduction Number

This study developed a model for the spread of COVID-19 disease using the SIR model which was added by a health mask and quarantine for infected individuals. The population is divided into six subpopulations, namely the subpopulation susceptible without a health mask, susceptible using a health mask, infected without using a health mask, infected using a health mask, quarantine for infected individuals, and the subpopulation to recover. The results obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point, and the basic reproduction number (R0). The existence of a disease-free equilibrium point is unconditional, whereas an endemic equilibrium point exists if the basic reproduction number is more than one. Stability analysis of the local asymptotically stable disease-free equilibrium point when the basic reproduction number is less than one. Furthermore, numerical simulations are carried out to provide a geometric picture related to the results that have been analyzed. The results of numerical simulations support the results of the analysis obtained. Finally, the sensitivity analysis of the basic reproduction numbers carried out obtained four parameters that dominantly affect the basic reproduction number, namely the rate of contact of susceptible individuals with infection, the rate of health mask use, the rate of health mask release, and the rate of quarantine for infected individuals.

Download Full-text

Analysis of COVID-19 based on SEIR epidemic models in a multi-patch environment

10.21203/rs.3.rs-306960/v1 ◽

2021 ◽

Author(s):

Lan Meng ◽

Wei Zhu

Keyword(s):

Numerical Simulations ◽

Dynamic Behavior ◽

Basic Reproduction Number ◽

Epidemic Model ◽

Migration Rate ◽

Reproduction Number ◽

Population Migration ◽

Theoretical Results ◽

Disease Free ◽

The Basic Reproduction Number

Abstract In this paper, an n-patch SEIR epidemic model for the coronavirus disease 2019 (COVID-19) is presented. It is shown that there is unique disease-free equilibrium for this model. Then, the dynamic behavior is studied by the basic reproduction number. Some numerical simulations with three patches are given to validate the effectiveness of the theoretical results. The influence of quarantined rate and population migration rate on the basic reproduction number is also discussed by simulation.

Download Full-text

Tuberculosis Model with Exogenous Reinfection and Treatment

Asian Research Journal of Mathematics ◽

10.9734/arjom/2020/v16i330181 ◽

2020 ◽

pp. 50-65

Author(s):

Ebenezer Appiagyei ◽

Mojeeb Al-Rahman El-Nor Osman ◽

Isaac Kwasi Adu

Keyword(s):

Global Stability ◽

Numerical Simulations ◽

Basic Reproduction Number ◽

Multiple Equilibria ◽

Reproduction Number ◽

Tuberculosis Model ◽

The Stability ◽

Disease Free ◽

Exogenous Reinfection ◽

The Basic Reproduction Number

The epidemiology of tuberculosis model, which includes exogenous reinfection and treatment, is analyzed. We consider both the diagnosed and the undiagnosed individuals as infectious. Since tuberculosis is treatable, we also included the treatment for diagnosed infective. We presented the basic reproduction number and the stability of the disease-free and endemic equilibria. We also analyzed the model when the exogenous re-infection is set to zero. The exogenous re-infection is shown to be capable of supporting multiple equilibria. Lastly, we presented the global stability and numerical simulations of the model.

Download Full-text

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

Abstract and Applied Analysis ◽

10.1155/2014/841367 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 3

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.

Download Full-text

Leptospirosis Public Health Education Campaign for the Rural Fijian Medical District of Nausori

SSRN Electronic Journal ◽

10.2139/ssrn.2437156 ◽

2014 ◽

Author(s):

Brian P. Mangum

Keyword(s):

Public Health ◽

Health Education ◽

Public Health Education ◽

Education Campaign

Download Full-text

Simple MSEIR Model for Measles Transmission

Asian Research Journal of Mathematics ◽

10.9734/arjom/2019/v12i330090 ◽

2019 ◽

pp. 1-11

Author(s):

Mojeeb Al-Rahman EL-Nor Osman ◽

Appiagyei Ebenezer ◽

Isaac Kwasi Adu

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Recovery Rate ◽

Birth Rate ◽

Reproduction Number ◽

Progression Rate ◽

Asymptotically Stable ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria. The basic reproduction number is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out. The disease was locally asymptotically stable if and unstable if . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

Download Full-text

On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

Applied Sciences ◽

10.3390/app10228296 ◽

2020 ◽

Vol 10 (22) ◽

pp. 8296 ◽

Cited By ~ 1

Author(s):

Malen Etxeberria-Etxaniz ◽

Santiago Alonso-Quesada ◽

Manuel De la Sen

Keyword(s):

Equilibrium Point ◽

Basic Reproduction Number ◽

Epidemic Model ◽

Disease Transmission ◽

Reproduction Number ◽

Equilibrium Points ◽

Endemic Equilibrium ◽

Impulsive Vaccination ◽

Disease Free ◽

The Basic Reproduction Number

This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

Download Full-text

Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Mathematics ◽

10.3390/math6120328 ◽

2018 ◽

Vol 6 (12) ◽

pp. 328 ◽

Cited By ~ 3

Author(s):

Yanli Ma ◽

Jia-Bao Liu ◽

Haixia Li

Keyword(s):

Lyapunov Function ◽

Basic Reproduction Number ◽

Epidemic Model ◽

Reproduction Number ◽

Endemic Equilibrium ◽

Global Dynamics ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Disease Free ◽

The Basic Reproduction Number

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

Download Full-text