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 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 Impact of Hygiene on Malaria Transmission Dynamics: A Mathematical Model

2021 ◽  
Author(s):  
Temidayo Oluwafemi ◽  
Emmanuel Azuaba
Keyword(s):  
Mathematical Model ◽  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Model System ◽  
Transmission Dynamics ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

Malaria continues to pose a major public health challenge, especially in developing countries, 219 million cases of malaria were estimated in 89 countries. In this paper, a mathematical model using non-linear differential equations is formulated to describe the impact of hygiene on Malaria transmission dynamics, the model is analyzed. The model is divided into seven compartments which includes five human compartments namely; Unhygienic susceptible human population, Hygienic Susceptible Human population, Unhygienic infected human population , hygienic infected human population and the Recovered Human population  and the mosquito population is subdivided into susceptible mosquitoes  and infected mosquitoes . The positivity of the solution shows that there exists a domain where the model is biologically meaningful and mathematically well-posed. The Disease-Free Equilibrium (DFE) point of the model is obtained, we compute the Basic Reproduction Number using the next generation method and established the condition for Local stability of the disease-free equilibrium, and we thereafter obtained the global stability of the disease-free equilibrium by constructing the Lyapunov function of the model system. Also, sensitivity analysis of the model system was carried out to identify the influence of the parameters on the Basic Reproduction Number, the result shows that the natural death rate of the mosquitoes is most sensitive to the basic reproduction number.

scholarly journals Mathematical Analysis of COVID-19 Transmission Dynamics with a Case Study of Nigeria and its Computer Simulation

2020 ◽  
Author(s):  
B. C. Agbata ◽  
Ogala Emmanuel ◽  
Tenuche Bashir ◽  
Obeng-Denteh William
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Government Policies ◽  
Asymptotically Stable ◽  
Deadly Disease ◽  
Next Generation Matrix ◽  
Disease Free ◽  
The Basic Reproduction Number

AbstractIn this article, we formulated a mathematical model for the spread of the COVID-19 disease and we introduced quarantined and isolated compartments. The next generation matrix method was adopted to compute the basic reproduction number (R0) in order to assess the transmission dynamics of the COVID-19 deadly disease. Stability analysis of the disease free equilibrium is investigated based on the basic reproduction number and the result shows that it is locally and asymptotically stable for R0 less than 1. Numerical calculation of the basic reproduction number revealed that R0 < 1 which means that the disease can be eradicated from Nigeria. The study shows that isolation, quarantine and other government policies like social distancing and lockdown are the best approaches to control the pernicious nature of COVID-19 pandemic.

scholarly journals Modeling the Transmission Dynamics of Measles in the Presence of Treatment as Control Strategy

2021 ◽  
pp. 76-86
Author(s):  
Rose Veronica Paul ◽  
William Atokolo ◽  
Salawu Ademu Saka ◽  
Achonu Omale Joseph
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Model Simulation ◽  
Research Work ◽  
Intervention Strategy ◽  
Transmission Dynamics ◽  
Disease Free ◽  
The Basic Reproduction Number

We present in this research work, mathematical modeling of the transmission dynamics of measles using treatment as a control measure. We determined the Disease Free Equilibrium (DFE) point of the model after which we obtained the Basic Reproduction Number ( R0 ) of the model using the next generation approach. The model Endemic Equilibrium (EE) point was also determined after which we performed Local Stability Analysis(LAS) of the Disease Free Equilibrium point and result shows that the Disease Free Equilibrium point of the model would be stable if ( R0 <1). Global Stability Analysis (GAS) result shows that, ( R0 ≤ 1) remains the necessary and sufficient condition for the infection to go into extinction from a population. We carried out Sensitivity Analysis of the model using the Basic Reproduction Number and we discovered that ( δ , μ, ν , θ ) are sensitive parameters that should be targeted towards control intervention strategy as an increase in these values can reduce the value of ( R0 ) to a value less than unity and such can reduce the spread of measles in a population. Model simulation was carried out using mat lab software to support our analytical results.

scholarly journals MATHEMATICAL ANALYSIS OF SENSITIVE PARAMETERS ON THE DYNAMICAL TRANSMISSION OF EBOLA HEMORRHAGIC FEVER

2016 ◽  
Vol 4 (10) ◽  
pp. 21-33
Author(s):  
Adewale ◽  
Adeniran ◽  
Olopade ◽  
Mohammed
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Hemorrhagic Fever ◽  
Relative Sensitivity ◽  
Medical Practitioners ◽  
Sensitivity Indices ◽  
Sensitive Parameters ◽  
Disease Free ◽  
The Basic Reproduction Number

A four (4) compartmental model of (S, E, I , I ) were presented to have better understanding of parameters that influence the dynamical spread of Ebola in a population. The model is analyzed for all the parameters responsible for the dynamical spread of the disease in order to find the most sensitive parameters that need to be given attention.  The stability of the model was analyzed for the existence of disease free and endemic equilibrium points. Basic Reproduction Number ( ) was obtained using next generation matrix method (NGM), and it is shown that the disease free equilibrium point is locally asymptotically stable whenever the basic reproduction number is less than unity i.e ( ) and unstable whenever the basic reproduction number is greater than unity ( ).The relative sensitivity indices of the model with respect to each parameter in the basic reproduction number is calculated in order to find the most sensitive parameter which the medical practitioners and policy health makers should work on in order to reduce the spread of Ebola in the population. The result shows that effective contact rate and fraction of individuals with low immunity are the most sensitive parameters in the reproduction number. Therefore, effort should be put in place so that the basic reproduction number should not be greater unity so as to prevent the endemic situation.

scholarly journals Analysis and Modeling of Tuberculosis Transmission Dynamics

2019 ◽  
pp. 1-14
Author(s):  
Rodah Jerubet ◽  
George Kimathi ◽  
Mary Wanaina
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Sensitive Parameter ◽  
Latently Infected ◽  
Model Equations ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

Mycobacterium tuberculosis is the causative agent of Tuberculosis in humans [1,2]. A mathematical model that explains the transmission of Tuberculosis is developed. The model consists of four compartments; the susceptible humans, the infectious humans, the latently infected humans, and the recovered humans. We conducted an analysis of the disease-free equilibrium and endemic equilibrium points. We also computed the basic reproduction number using the next generation matrix approach. The disease-free equilibrium was found to be asymptotically stable if the reproduction number was less than one. The most sensitive parameter to the basic reproduction number was also determined using sensitivity analysis. Recruitment and contact rate are the most sensitive parameter that contributes to the basic reproduction number. Ordinary Differential Equations is used in the for­mulation of the model equations. The Tuberculosis model is analyzed in order to give a proper account of the impact of its transmission dynamics and the effect of the latent stage in TB transmission. The steady state's solution of the model is investigated. The findings showed that as more people come into contact with infectious individuals, the spread of TB would increase. The latent rate of infection below a critical value makes TB infection to persist.   However, the recovery rate of infectious individuals is an indication that the spread of the disease will reduce with time which could help curb TB transmission. 

scholarly journals COVID-19 Transmission Dynamics and Final Epidemic Size

2020 ◽  
Author(s):  
Daifeng Duan ◽  
Cuiping Wang ◽  
Yuan Yuan
Keyword(s):  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Epidemic Size ◽  
Final Epidemic Size ◽  
The Common ◽  
Potential Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract We propose two kinds of compartment models to study the transmission dynamics of COVID-19 virus and to explore the potential impact of the interventions, to disentangle how transmission is affected in different age group. Starting with an SEAIQR model by combining the effect from exposure, asymptomatic and quarantine, then extending the model to an two groups with ages below and above 65 years old, and classify the infectious individuals according to their severity, we focus our analysis on each model with and without vital dynamics. In the models with vital dynamics, we study the dynamical properties including the global stability of the disease free equilibrium and the existence of endemic equilibrium, with respect to the basic reproduction number. Whereas in the models without vital dynamics, we address the final epidemic size rigorously, which is one of the common but difficult questions regarding an epidemic. Finally, using the data of COVID-19 confirmed cases in Canada and Newfoundland & Labrador province, we can parameterize the models to estimate the basic reproduction number and the final epidemic size of disease transmission.

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 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 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

2020 ◽  
Vol 10 (22) ◽  
pp. 8296 ◽  
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.

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