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 A Mathematical Model of COVID-19 Pandemic: A Case Study of Bangkok, Thailand

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Pakwan Riyapan ◽  
Sherif Eneye Shuaib ◽  
Arthit Intarasit
Keyword(s):  
Mathematical Model ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Proposed Model ◽  
Next Generation Matrix ◽  
Disease Free ◽  
The Basic Reproduction Number

In this study, we propose a new mathematical model and analyze it to understand the transmission dynamics of the COVID-19 pandemic in Bangkok, Thailand. It is divided into seven compartmental classes, namely, susceptible S , exposed E , symptomatically infected I s , asymptomatically infected I a , quarantined Q , recovered R , and death D , respectively. The next-generation matrix approach was used to compute the basic reproduction number denoted as R cvd 19 of the proposed model. The results show that the disease-free equilibrium is globally asymptotically stable if R cvd 19 < 1 . On the other hand, the global asymptotic stability of the endemic equilibrium occurs if R cvd 19 > 1 . The mathematical analysis of the model is supported using numerical simulations. Moreover, the model’s analysis and numerical results prove that the consistent use of face masks would go on a long way in reducing the COVID-19 pandemic.

scholarly journals Stability Analysis of the Disease Free Equilibrium of Malaria, Dengue and Typhoid Triple Infection Model

2020 ◽  
pp. 15-23
Author(s):  
T. J. Oluwafemi ◽  
E. Azuaba ◽  
Y. M. Kura
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Infection Model ◽  
Triple Infection ◽  
Next Generation Matrix ◽  
Linear Differential ◽  
Disease Free ◽  
The Basic Reproduction Number

A Mathematical model of a system of non-linear differential equation is developed to study the transmission dynamics of malaria, dengue and typhoid triple infection. In this work, the basic reproduction number is derived using the Next Generation Matrix, also we computed the disease free equilibrium point. The disease free equilibrium (DFE) point is analyzed and was found that the DFE is locally stable but may be globally unstable when R0 < 1.

scholarly journals Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

scholarly journals Dynamics Analysis of an Avian Influenza A (H7N9) Epidemic Model with Vaccination and Seasonality

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Juping Zhang ◽  
Yun Li ◽  
Zhen Jin ◽  
Huaiping Zhu
Keyword(s):  
Avian Influenza ◽  
Influenza A ◽  
Reproduction Number ◽  
Positive Periodic Solution ◽  
Human Infection ◽  
Transmission Model ◽  
H7n9 Infection ◽  
Simulation Results ◽  
Theoretical Results ◽  
Disease Free

H7N9 virus in the environment plays a role in the dynamics of avian influenza A (H7N9). A nationwide poultry vaccination with H7N9 vaccine program was implemented in China in October of 2017. To analyze the effect of vaccination and environmental virus on the development of avian influenza A (H7N9), we establish an avian influenza A (H7N9) transmission model with vaccination and seasonality among human, birds, and poultry. The basic reproduction number for the prevalence of avian influenza is obtained. The global stability of the disease-free equilibrium and the existence of positive periodic solution are proved by the comparison theorem and the asymptotic autonomous system theorem. Finally, we use numerical simulations to demonstrate the theoretical results. Simulation results indicate that the risk of H7N9 infection is higher in colder environment. Vaccinating poultry can significantly reduce human infection.

scholarly journals Stability of a Mathematical Model of Malaria Transmission with Relapse

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hai-Feng Huo ◽  
Guang-Ming Qiu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Next Generation Matrix ◽  
The Government ◽  
Disease Free ◽  
The Basic Reproduction Number

A more realistic mathematical model of malaria is introduced, in which we not only consider the recovered humans return to the susceptible class, but also consider the recovered humans return to the infectious class. The basic reproduction numberR0is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable ifR0≤1, and the system is uniformly persistence ifR0>1. Some numerical simulations are also given to explain our analytical results. Our results show that to control and eradicate the malaria, it is very necessary for the government to decrease the relapse rate and increase the recovery rate.

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 SIARD Model and Effect of Lockdown on the Dynamics of COVID-19 Disease with non Total Immunity

2021 ◽  
Author(s):  
Radouane Yafia
Keyword(s):  
Mathematical Model ◽  
Local Stability ◽  
Reproduction Number ◽  
Special Focus ◽  
System Of Differential Equations ◽  
French Case ◽  
Sensitive Parameters ◽  
Theoretical Results ◽  
Epidemic Wave ◽  
The Basic Reproduction Number

We propose a new compartmental mathematical model describing the transmission and the spreading of COVID -19 epidemic with a special focus on the non-total immunity. The model \textit {(called SIARD )} is given by a system of differential equations which model the interactions between five populations "susceptible", "reported infectious", "unreported infectious", "recovered with/without non total immunity" and "death". Depending on the basic reproduction number, we prove that the total immunity induces local stability-instability of equilibria and the epidemic may disappear after a first epidemic wave and more epidemic waves may appear in the case of non-total immunity. Using the sensitivity analysis we identify the most sensitive parameters. Numerical simulations are carried out to illustrate our theoretical results. As an application, we found that our model fits well the Moroccan epidemic wave, and predicts more than one wave for French case.

scholarly journals Mathematical Model of the Transmission Dynamics of Corona Virus Disease (COVID-19) and Its Control

2021 ◽  
pp. 69-88
Author(s):  
Atokolo William ◽  
Omale David ◽  
Bashir Sezuo Tenuche ◽  
Olayemi Kehinde Samuel ◽  
Daniel Musa Alih ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium State ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Control Measure ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Corona Virus ◽  
The Basic Reproduction Number

This work is aimed at formulating a mathematical model for the transmission dynamics and control of corona virus disease in a population. The Disease Free Equilibrium state of the model was determined and shown to be locally asymptotically stable. The Endemic Equilibrium state of the model was also established and proved to be locally asymptotically stable using the trace and determinant method, after which we determined the basic reproduction number ( ) of the model using the next generation method. When ( ), the disease is wiped out of a population, but if ( ), the disease invades such population. Local sensitivity analysis result shows that the rate at which the exposed are quarantined ( ), the rate at which the infected are isolated ( ), the rate at which the quarantined are isolated ( ), and the treatment rate ( ) should be targeted by the control intervention strategies as an increase in the values of these parameters (  and ) will reduce the basic reproduction number  ( ) of the COVID-19 and as such will eliminate the disease from the population with time. Numerical simulation of the model shows that the disease will be eradicated with time when enlightenment control measure for the susceptible individuals to observe social distance, frequent use of hand sanitizers, covering of mouth when coughing or sneezing are properly observed. Moreso, increasing the rates at which the suspected and confirmed cases of COVID-19 are quarantined and isolated respectively reduce the spread of the global pandemic.

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 Global Dynamics of Avian Influenza Epidemic Models with Psychological Effect

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sanhong Liu ◽  
Liuyong Pang ◽  
Shigui Ruan ◽  
Xinan Zhang
Keyword(s):  
Avian Influenza ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Influenza A ◽  
Reproduction Number ◽  
Psychological Effect ◽  
Saturation Effect ◽  
Effective Control ◽  
Global Dynamics ◽  
The Basic Reproduction Number

Cross-sectional surveys conducted in Thailand and China after the outbreaks of the avian influenza A H5N1 and H7N9 viruses show a high degree of awareness of human avian influenza in both urban and rural populations, a higher level of proper hygienic practice among urban residents, and in particular a dramatically reduced number of visits to live markets in urban population after the influenza A H7N9 outbreak in China in 2013. In this paper, taking into account the psychological effect toward avian influenza in the human population, a bird-to-human transmission model in which the avian population exhibits saturation effect is constructed. The dynamical behavior of the model is studied by using the basic reproduction number. The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent. Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.

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