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 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 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.

Mathematical Study of a Class of Epidemiological Models with Multiple Infectious Stages

2020 ◽  
Vol 21 (3-4) ◽  
pp. 259-274
Author(s):  
S. Bowong ◽  
A. Temgoua ◽  
Y. Malong ◽  
J. Mbang
Keyword(s):  
Theoretical Study ◽  
Reproduction Number ◽  
Communicable Disease ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Epidemiological Models ◽  
Mathematical Study ◽  
Globally Asymptotically Stable ◽  
Disease Free

AbstractThis paper deals with the mathematical analysis of a general class of epidemiological models with multiple infectious stages for the transmission dynamics of a communicable disease. We provide a theoretical study of the model. We derive the basic reproduction number $\mathcal R_0$ that determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever $\mathcal R_0 \leq 1$, while when $\mathcal R_0 \gt 1$, the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. A case study for tuberculosis (TB) is considered to numerically support the analytical results.

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 Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination

2021 ◽  
Vol 4 (2) ◽  
pp. 106-124
Author(s):  
Raqqasyi Rahmatullah Musafir ◽  
Agus Suryanto ◽  
Isnani Darti
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Asymptomatic Infection ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Proposed Model ◽  
Disease Free ◽  
The Basic Reproduction Number

We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V ). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points.

scholarly journals Dynamics of A Multi-stage Epidemic Model with and without Treatment

2020 ◽  
Vol 8 (5) ◽  
pp. 5293-5300
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Dynamical Behaviour ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, a non-linear mathematical model is proposed with the thought of treatment to depict the spread of infectious illness and assessed with three contamination stages. We talk about the dynamical behaviour and analytical study of the framework for the mathematical model which shows that it has two non-negative equilibrium points i.e., disease-free equilibrium (DFE) and interior(endemic) equilibrium. The outcomes show that the dynamical behaviour of the model is totally determined by the basic reproduction number. For the basic reproduction number , the disease-free equilibrium is locally as well as globally asymptotically stable under a particular parameter set. In case , the model at the interior equilibrium is locally as well as globally asymptotically stable. Finally, numerical solutions of the model corroborate the analytical results and facilitate a sensitivity analysis of the model parameters.

scholarly journals Mathematical Model of Cholera Transmission with Education Campaign and Treatment Through Quarantine

2019 ◽  
pp. 1-12
Author(s):  
H. O. Nyaberi ◽  
D. M. Malonza
Keyword(s):  
Mathematical Model ◽  
Health Education ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Watery Diarrhea ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Education Campaign ◽  
Next Generation Matrix ◽  
Disease Free

Cholera, a water-borne disease characterized by intense watery diarrhea, affects people in the regions with poor hygiene and untreated drinking water. This disease remains a menace to public health globally and it indicates inequity and lack of community development. In this research, SIQR-B mathematical model based on a system of ordinary differential equations is formulated to study the dynamics of cholera transmission with health education campaign and treatmentthrough quarantine as controls against epidemic in Kenya. The effective basic reproduction number is computed using the next generation matrix method. The equilibrium points of the model are determined and their stability is analysed. Results of stability analysis show that the disease free equilibrium is both locally and globally asymptotically stable R0 < 1 while the endemic equilibrium is both locally and globally asymptotically stable R0 > 1. Numerical simulation carried out using MATLAB software shows that when health education campaign is efficient, the number of cholera infected individuals decreases faster, implying that health education campaign is vital in controlling the spread of cholera disease.

scholarly journals Mathematical Model and Analysis of Corruption Dynamics with Optimal Control

2022 ◽  
Vol 2022 ◽  
pp. 1-16
Author(s):  
Abayneh Kebede Fantaye ◽  
Zerihun Kinfe Birhanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Reproduction Number ◽  
Control Model ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Next Generation Matrix ◽  
Boundedness Of Solution ◽  
Positivity And Boundedness

In this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number R 0 is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever R 0 < 1 . Also, the endemic equilibrium point is locally and globally asymptotically stable whenever R 0 > 1 . Then, the model was extended to optimal control, and some numerical simulations with and without optimal control are also performed to verify the theoretical analysis using MATLAB. Numerical simulation of optimal control model shows that the prevention and punishment strategy is the most effective strategy to reduce the dynamic transmission of corruption.

scholarly journals Global Stability of a SLIT TB Model with Staged Progression

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yakui Xue ◽  
Xiaohong Wang
Keyword(s):  
Mathematical Model ◽  
Latent Period ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Infectious Period ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
N Stage ◽  
Disease Free ◽  
The Basic Reproduction Number

Because the latent period and the infectious period of tuberculosis (TB) are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression (SP) model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reproduction numberR0. Moreover, ifR0≤1, the disease-free equilibriumP0is globally asymptotically stable and the disease always dies out. IfR0>1, the unique endemic equilibriumP∗is globally asymptotically stable and the disease persists at the endemic equilibrium.

scholarly journals Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Achamyelesh Amare Aligaz ◽  
Justin Manango W. Munganga
Keyword(s):  
Mathematical Model ◽  
Antibiotic Treatment ◽  
Reproduction Number ◽  
Threshold Value ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Contagious Bovine Pleuropneumonia ◽  
Sharp Threshold ◽  
Globally Asymptotically Stable ◽  
Disease Free

In this paper we present a mathematical model for the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by considering antibiotic treatment and vaccination. The model is comprised of susceptible, vaccinated, exposed, infectious, persistently infected, and recovered compartments. We analyse the model by deriving a formula for the control reproduction number Rc and prove that, for Rc<1, the disease free equilibrium is globally asymptotically stable; thus CBPP dies out, whereas for Rc>1, the unique endemic equilibrium is globally asymptotically stable and hence the disease persists. Thus, Rc=1 acts as a sharp threshold between the disease dying out or causing an epidemic. As a result, the threshold of antibiotic treatment is αt⁎=0.1049. Thus, without using vaccination, more than 85.45% of the infectious cattle should receive antibiotic treatment or the period of infection should be reduced to less than 8.15 days to control the disease. Similarly, the threshold of vaccination is ρ⁎=0.0084. Therefore, we have to vaccinate at least 80% of susceptible cattle in less than 49.5 days, to control the disease. Using both vaccination and antibiotic treatment, the threshold value of vaccination depends on the rate of antibiotic treatment, αt, and is denoted by ραt. Hence, if 50% of infectious cattle receive antibiotic treatment, then at least 50% of susceptible cattle should get vaccination in less than 73.8 days in order to control the disease.

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