scholarly journals A Mathematical Model for Coinfection of Listeriosis and Anthrax Diseases

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Shaibu Osman ◽  
Oluwole Daniel Makinde
Keyword(s):  
Human Population ◽  
Reproduction Number ◽  
Zoonotic Diseases ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Contact Rate ◽  
Disease Dynamics ◽  
Human Contact ◽  
The Stability ◽  
Disease Free

Listeriosis and Anthrax are fatal zoonotic diseases caused by Listeria monocytogene and Bacillus Anthracis, respectively. In this paper, we proposed and analysed a compartmental Listeriosis-Anthrax coinfection model describing the transmission dynamics of Listeriosis and Anthrax epidemic in human population using the stability theory of differential equations. Our model revealed that the disease-free equilibrium of the Anthrax model only is locally stable when the basic reproduction number is less than one. Sensitivity analysis was carried out on the model parameters in order to determine their impact on the disease dynamics. Numerical simulation of the coinfection model was carried out and the results are displayed graphically and discussed. We simulate the Listeriosis-Anthrax coinfection model by varying the human contact rate to see its effects on infected Anthrax population, infected Listeriosis population, and Listeriosis-Anthrax coinfected population.

Analysis of a mathematical model for the transmission dynamics of human melioidosis

2020 ◽  
Vol 13 (07) ◽  
pp. 2050062
Author(s):  
Yibeltal Adane Terefe ◽  
Semu Mitiku Kassa
Keyword(s):  
Human Population ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Disease Dynamics ◽  
Number Formula ◽  
Disease Free

A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the basic reproduction number [Formula: see text] is less than one. It is further shown that the backward bifurcation dynamics is caused by the reinfection of individuals who recovered from the disease and relapse. The existence of backward bifurcation implies that bringing down [Formula: see text] to less than unity is not enough for disease eradication. In the absence of backward bifurcation, the global asymptotic stability of the disease-free equilibrium is shown whenever [Formula: see text]. For [Formula: see text], the existence of at least one locally asymptotically stable endemic equilibrium is shown. Sensitivity analysis of the model, using the parameters relevant to the transmission dynamics of the melioidosis disease, is discussed. Numerical experiments are presented to support the theoretical analysis of the model. In the numerical experimentations, it has been observed that screening and treating individuals in the exposed class has a significant impact on the disease dynamics.

scholarly journals A Theoretical Model for the Transmission Dynamics of the Buruli Ulcer with Saturated Treatment

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ebenezer Bonyah ◽  
Isaac Dontwi ◽  
Farai Nyabadza
Keyword(s):  
Human Population ◽  
Reproduction Number ◽  
Buruli Ulcer ◽  
Coupled System ◽  
Model Parameters ◽  
The Public ◽  
Treatment Function ◽  
Medical Facilities ◽  
The Stability ◽  
Saturated Treatment

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

scholarly journals Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Hailay Weldegiorgis Berhe ◽  
Oluwole Daniel Makinde ◽  
David Mwangi Theuri
Keyword(s):  
Sensitivity Analysis ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Nonlinear Least Squares ◽  
Model Parameters ◽  
Nonlinear Least Squares Problem ◽  
The Stability ◽  
Diarrhea Disease ◽  
Effective Transmission ◽  
Disease Free

In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease-free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for R0>1. The system is formulated as a standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is R0=1.1208. This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea (βh). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.

scholarly journals Dynamics of swine influenza model with optimal control

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Takasar Hussain ◽  
Muhammad Ozair ◽  
Kazeem Oare Okosun ◽  
Muhammad Ishfaq ◽  
Aziz Ullah Awan ◽  
...  
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Swine Influenza ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
And Control ◽  
Disease Free ◽  
Good Agreement

AbstractTransmission dynamics of swine influenza pandemic is analysed through a deterministic model. Qualitative analysis of the model includes global asymptotic stability of disease-free and endemic equilibria under a certain condition based on the reproduction number. Sensitivity analysis to ponder the effect of model parameters on the reproduction number is performed and control strategies are designed. It is also verified that the obtained numerical results are in good agreement with the analytical ones.

scholarly journals Mathematical modelling of pneumonia dynamics of children under the age of five

2021 ◽  
Author(s):  
Idowu Kabir Oluwatobi ◽  
Erinle-Ibrahim L.M
Keyword(s):  
Mathematical Modelling ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Natural Immunity ◽  
Paper Work ◽  
Effect Of Treatment ◽  
The Stability ◽  
Disease Free

Abstract This paper work was designed to study the effect of treatment on the transmission of pneumonia infection. When studying the transmission dynamics of infectious diseases with an objective of suggesting control measures, it is important to consider the stability of equilibrium points. In this paper, basic reproduction number, effective reproduction number, existences and stability of the equilibrium point were established.Using Lyaponov function we discovered that the disease free equilibrium is unstable. The results are presented in graphs and it is discovered that the spread of the infection will be greatly affected by the rate of treatment and natural immunity.

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.

Assessing the impact of transmissibility on a cluster-based COVID-19 model in India

2021 ◽  
pp. 2141002
Author(s):  
Tanvi ◽  
Mohammad Sajid ◽  
Rajiv Aggarwal ◽  
Ashutosh Rajput
Keyword(s):  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Nonlinear Mathematical Model ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
The Stability ◽  
The Impact ◽  
Disease Free

In this paper, we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus (COVID-19). The model incorporates the effect of transmission and treatment on the occurrence of new infections. For the model, the basic reproduction number [Formula: see text] has been computed. Corresponding to the threshold quantity [Formula: see text], the stability of endemic and disease-free equilibrium (DFE) points are determined. For [Formula: see text], if the endemic equilibrium point exists, then it is locally asymptotically stable, whereas the DFE point is globally asymptotically stable for [Formula: see text] which implies the eradication of the disease. The effects of various parameters on the spread of COVID-19 are discussed in the segment of sensitivity analysis. The model is numerically simulated to understand the effect of reproduction number on the transmission dynamics of the disease COVID-19. From the numerical simulations, it is concluded that if the reproduction number for the coronavirus disease is reduced below unity by decreasing the transmission rate and detecting more number of infectives, then the epidemic can be eradicated from the population.

scholarly journals Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control.

2020 ◽  
Vol 51 (4) ◽  
pp. 261-287
Author(s):  
Shaibu Osman ◽  
Oluwole Daniel Makinde ◽  
David Mwangi Theuri
Keyword(s):  
Optimal Control ◽  
Human Population ◽  
Model Problem ◽  
Control Strategies ◽  
Model Parameters ◽  
Contaminated Food ◽  
Serious Disease ◽  
The Stability ◽  
The Impact ◽  
Disease Free

Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.

scholarly journals Parameter Estimation of COVID-19 Pandemic Model with Self Protection Behavior Changes

2020 ◽  
Author(s):  
Kassahun Getnet Mekonen ◽  
Tatek Getachew Habtemicheal ◽  
Shiferaw Feyissa Balcha
Keyword(s):  
Equilibrium Point ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Estimation Methods ◽  
Behavior Changes ◽  
Model Parameters ◽  
Sensitivity Index ◽  
Self Protection ◽  
Sensitive Parameters ◽  
Disease Free

A mathematical model for the transmission dynamics of Coronavirus diseases (COVID-19) is proposed by incorporating self-protection behavior changes in the population. The disease-free equilibrium point is computed and its stability analysis is studied. The basic reproduction number(R 0 ) of the model is computed and the disease-free equilibrium point is locally and globally stable for R 0<1 and unstable for R 0 >1. Based on the available data the unknown model parameters are estimated using a combination of least square and Bayesian estimation methods for different countries. Using forward sensitivity index the model parameters are carried out to determine and identify the key factors for the spread of disease dynamics. From country to country the sensitive parameters for the spread of the virus varies. It is found out that the reproduction number depends mostly on the infection rates, the threshold value of the force of infection for a population, the recovery rates, and the virus decay rate in the environment. It is also demonstrated that control of the effective transmission rate (recommended human behavioral change towards self-protective measures) is essential to stop the spreading of the virus. Numerical simulations also show that the virus transmission dynamics depend mostly on those sensitive parameters.

scholarly journals Mathematical Model of the Transmission Dynamics of Novel Corona Virus (COVID-19) Pandamic Disease with Optimal Control

2021 ◽  
Vol 15 ◽  
pp. 195-214
Author(s):  
Getachew Beyecha Batu ◽  
Eshetu Dadi Gurmu
Keyword(s):  
Mathematical Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Relative Significance ◽  
Corona Virus ◽  
Next Generation Matrix ◽  
The Stability ◽  
Disease Free

In this paper, we have developed a deterministic mathematical model that discribe the transmission dynamics of novel corona virus with prevention control. The disease free and endemic equilibrium point of the model were calculated and its stability analysis were prformed. The reproduction number R0 of the model which determine the persistence of the disease or not was calculated by using next generation matrix and also used to determine the stability of the disease free and endemic equilibrium points which exists conditionally. Furthermore, sensitivity analysis of the model was performed on the parameters in the equation of reproduction to determine their relative significance on the transmission dynamics of COVID- 19 pandemic disease. Finally the simulations were carried out using MATLAB R2015b with ode45 solver. The simulation results illustrated that applying prevention control can successfully reduces the transmission dynamic of COVID-19 infectious disease.

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