MODELING CHOLERA DISEASE WITH EDUCATION AND CHLORINATION

2013 ◽  
Vol 21 (04) ◽  
pp. 1340007 ◽  
Author(s):  
MO'TASSEM AL-ARYDAH ◽  
ABUBAKAR MWASA ◽  
JEAN M. TCHUENCHE ◽  
ROBERT J. SMITH?
Keyword(s):  
Infectious Disease ◽  
Reproduction Number ◽  
Latin Hypercube Sampling ◽  
Control Measures ◽  
Effective Control ◽  
Severe Diarrhea ◽  
Water Chlorination ◽  
Disease Free ◽  
The Basic Reproduction Number ◽  
Water Borne

Cholera, characterized by severe diarrhea and rapid dehydration, is a water-borne infectious disease caused by the bacterium Vibrio cholerae. Haiti offers the most recent example of the tragedy that can befall a country and its people when cholera strikes. While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate and analyze a mathematical model that includes two essential and affordable control measures: water chlorination and education. We calculate the basic reproduction number and determine the global stability of the disease-free equilibrium for the model without chlorination. We use Latin Hypercube Sampling to demonstrate that the model is most sensitive to education. We also derive the minimal effective chlorination period required to control the disease for both fixed and variable chlorination. Numerical simulations suggest that education is more effective than chlorination in decreasing bacteria and the number of cholera cases.

scholarly journals Estimating the basic reproduction number for the 2015 bubonic plague outbreak in Nyimba district of Eastern Zambia

2020 ◽  
Vol 14 (11) ◽  
pp. e0008811
Author(s):  
Joseph Sichone ◽  
Martin C. Simuunza ◽  
Bernard M. Hang’ombe ◽  
Mervis Kikonko
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Cost Effective ◽  
Control Measures ◽  
Effective Control ◽  
Infectious Period ◽  
Bubonic Plague ◽  
Infectious Individual ◽  
Susceptible Population ◽  
The Basic Reproduction Number

Background Plague is a re-emerging flea-borne infectious disease of global importance and in recent years, Zambia has periodically experienced increased incidence of outbreaks of this disease. However, there are currently no studies in the country that provide a quantitative assessment of the ability of the disease to spread during these outbreaks. This limits our understanding of the epidemiology of the disease especially for planning and implementing quantifiable and cost-effective control measures. To fill this gap, the basic reproduction number, R0, for bubonic plague was estimated in this study, using data from the 2015 Nyimba district outbreak, in the Eastern province of Zambia. R0 is the average number of secondary infections arising from a single infectious individual during their infectious period in an entirely susceptible population. Methodology/Principal findings Secondary epidemic data for the most recent 2015 Nyimba district bubonic plague outbreak in Zambia was analyzed. R0 was estimated as a function of the average epidemic doubling time based on the initial exponential growth rate of the outbreak and the average infectious period for bubonic plague. R0 was estimated to range between 1.5599 [95% CI: 1.382–1.7378] and 1.9332 [95% CI: 1.6366–2.2297], with average of 1.7465 [95% CI: 1.5093–1.9838]. Further, an SIR deterministic mathematical model was derived for this infection and this estimated R0 to be between 1.4 to 1.5, which was within the range estimated above. Conclusions/Significance This estimated R0 for bubonic plague is an indication that each bubonic plague case can typically give rise to almost two new cases during these outbreaks. This R0 estimate can now be used to quantitatively analyze and plan measurable interventions against future plague outbreaks in Zambia.

scholarly journals Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics

2020 ◽  
Author(s):  
S. Olaniyi ◽  
O.S. Obabiyi ◽  
K.O. Okosun ◽  
A.T. Oladipo ◽  
S.O. Adewale
Keyword(s):  
Basic Reproduction Number ◽  
Least Squares Method ◽  
Reproduction Number ◽  
Cost Effective ◽  
Effective Control ◽  
Cumulative Number ◽  
The Novel ◽  
Novel Coronavirus ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract The novel coronavirus disease (COVID-19) caused by a new strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remains the current global health challenge. In this paper, an epidemic model based on system of ordinary differential equations is formulated by taking into account the transmission routes from symptomatic, asymptomatic and hospitalized individuals. The model is fitted to the corresponding cumulative number of hospitalized individuals (active cases) reported by the Nigeria Centre for Disease Control (NCDC), and parameterized using the least squares method. The basic reproduction number which measures the potential spread of COVID-19 in the population is computed using the next generation operator method. Further, Lyapunov function is constructed to investigate the stability of the model around a disease-free equilibrium point. It is shown that the model has a globally asymptotically stable disease-free equilibrium if the basic reproduction number of the novel coronavirus transmission is less than one. Sensitivities of the model to changes in parameters are explored. It is revealed further that the basic reproduction number can be brought to a value less than one in Nigeria, if the current effective transmission rate of the disease can be reduced by 50%. Otherwise, the number of active cases may get up to 2.5% of the total estimated population. In addition, two time-dependent control variables, namely preventive and management measures, are considered to mitigate the damaging effects of the disease using Pontryagin's maximum principle. The most cost-effective control measure is determined through cost-effectiveness analysis. Numerical simulations of the overall system are implemented in MatLab® for demonstration of the theoretical results.

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

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.

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.

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 Inferring R 0 in emerging epidemics—the effect of common population structure is small

2016 ◽  
Vol 13 (121) ◽  
pp. 20160288 ◽  
Author(s):  
Pieter Trapman ◽  
Frank Ball ◽  
Jean-Stéphane Dhersin ◽  
Viet Chi Tran ◽  
Jacco Wallinga ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Population Structure ◽  
Robust Control ◽  
Reproduction Number ◽  
Contact Structures ◽  
Emerging Infections ◽  
Control Effort ◽  
Large Outbreak ◽  
Epidemiological Parameters ◽  
The Basic Reproduction Number

When controlling an emerging outbreak of an infectious disease, it is essential to know the key epidemiological parameters, such as the basic reproduction number R 0 and the control effort required to prevent a large outbreak. These parameters are estimated from the observed incidence of new cases and information about the infectious contact structures of the population in which the disease spreads. However, the relevant infectious contact structures for new, emerging infections are often unknown or hard to obtain. Here, we show that, for many common true underlying heterogeneous contact structures, the simplification to neglect such structures and instead assume that all contacts are made homogeneously in the whole population results in conservative estimates for R 0 and the required control effort. This means that robust control policies can be planned during the early stages of an outbreak, using such conservative estimates of the required control effort.

scholarly journals Mathematical Analysis of an Immune-structured Hikungunya Transmission Model

2019 ◽  
Vol 12 (4) ◽  
pp. 1533-1552
Author(s):  
Kambire Famane ◽  
Gouba Elisée ◽  
Tao Sadou ◽  
Blaise Some
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Transmission Model ◽  
Acquired Immunity ◽  
Local Asymptotic Stability ◽  
Well Posed ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we have formulated a new deterministic model to describe the dynamics of the spread of chikunguya between humans and mosquitoes populations. This model takes into account the variation in mortality of humans and mosquitoes due to other causes than chikungunya disease, the decay of acquired immunity and the immune sytem boosting. From the analysis, itappears that the model is well posed from the mathematical and epidemiological standpoint. The existence of a single disease free equilibrium has been proved. An explicit formula, depending on the parameters of the model, has been obtained for the basic reproduction number R0 which is used in epidemiology. The local asymptotic stability of the disease free equilibrium has been proved. The numerical simulation of the model has confirmed the local asymptotic stability of the diseasefree equilbrium and the existence of endmic equilibrium. The varying effects of the immunity parameters has been analyzed numerically in order to provide better conditions for reducing the transmission of the disease.

scholarly journals Simple MSEIR Model for Measles Transmission

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.

scholarly journals Global dynamics of a Huanglongbing model with a periodic latent period

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yan Hong ◽  
Xiuxiang Liu ◽  
Xiao Yu
Keyword(s):  
Reproduction Number ◽  
Threshold Value ◽  
Transmission Model ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Temperature Dependent ◽  
Candidatus Liberibacter ◽  
Effects Of Temperature ◽  
Disease Free ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>Huanglongbing (HLB) is a disease of citrus that caused by phloem-restricted bacteria of the Candidatus Liberibacter group. In this paper, we present a HLB transmission model to investigate the effects of temperature-dependent latent periods and seasonality on the spread of HLB. We first establish disease free dynamics in terms of a threshold value <inline-formula><tex-math id="M1">\begin{document}$ R^p_0 $\end{document}</tex-math></inline-formula>, and then introduce the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> and show the threshold dynamics of HLB with respect to <inline-formula><tex-math id="M3">\begin{document}$ R^p $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>. Numerical simulations are further provided to illustrate our analytic results.</p>

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