A Mathematical Model of the Transmission Dynamics of Bovine Schistosomiasis with Contaminated Environment

2022 ◽  
Vol 70 (1) ◽  
Author(s):  
Solomon Kadaleka ◽  
Shirley Abelman ◽  
Jean M. Tchuenche
Keyword(s):  
Mathematical Model ◽  
Transmission Dynamics ◽  
Bovine Schistosomiasis

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

scholarly journals Modeling the spread of porcine reproductive and respiratory syndrome virus (PRRSV) in a swine population: transmission dynamics, immunity information, and optimal control strategies

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Phithakdet Phoo-ngurn ◽  
Chanakarn Kiataramkul ◽  
Farida Chamchod
Keyword(s):  
Mathematical Model ◽  
Vaccination Coverage ◽  
Control Strategies ◽  
Vaccination Rate ◽  
Transmission Dynamics ◽  
Respiratory Syndrome Virus ◽  
Respiratory Problems ◽  
Prrs Virus ◽  
Swine Population ◽  
Swine Disease

Abstract Porcine reproductive and respiratory syndrome (PRRS) is an important swine disease that affects many swine industries worldwide. The disease can cause reproductive failure and respiratory problems in a swine population. As vaccination is an important tool to control the spread of PRRS virus (PRRSV), we employ a mathematical model to investigate the transmission dynamics of PRRSV and the effects of immunity information, as well as vaccination control strategies. We also explore optimal vaccination coverage and vaccination rate to minimize the number of infected swines and vaccination efforts. Our results suggest that: (i) higher vaccination coverage and vaccination rate together with prior knowledge about immunity may help reduce the prevalence of PRRSV, and (ii) longer maximum vaccination efforts are required when swines stay longer in a population and it takes them longer time to recover from PRRS infections.

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 Estimasi Reproduction Number Model Matematika Penyebaran Malaria di Sumba Tengah, Indonesia

2021 ◽  
Vol 2 (1) ◽  
pp. 13-19
Author(s):  
Ervin Mawo Banni ◽  
Maria A Kleden ◽  
Maria Lobo ◽  
Meksianis Zadrak Ndii
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Health Center ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Awareness Program ◽  
Awareness Programs ◽  
Malaria Eradication

Malaria is transmitted via a bite of mosquitoes and it is dangerous if it is not properly treated. Mathematical modeling can be formulated to understand the disease transmission dynamics. In this paper, a mathematical model with an awareness program has been formulated and the reproduction number has been estimated against the data from Weeluri Health Center, Mamboro District, Central Sumba. The calculation showed that the reproduction number is R0 = 1.2562. Results showed that if the efficacy of the awareness program is lower than 20%, the reproduction number is still above unity. If the efficacy of the awareness program is higher than 20%, the reproduction number is lower than unity. This implies that the efficacy of awareness programs is the key to the success of Malaria eradication.

scholarly journals A mathematical model for COVID-19 transmission dynamics with a case study of India

2020 ◽  
Vol 140 ◽  
pp. 110173 ◽  
Author(s):  
Piu Samui ◽  
Jayanta Mondal ◽  
Subhas Khajanchi
Keyword(s):  
Mathematical Model ◽  
Transmission Dynamics

scholarly journals A MATHEMATICAL MODEL FOR EBOLA EPIDEMIC WITH SELF-PROTECTION MEASURES

2018 ◽  
Vol 26 (01) ◽  
pp. 107-131 ◽  
Author(s):  
T. BERGE ◽  
M. CHAPWANYA ◽  
J. M.-S. LUBUMA ◽  
Y. A. TEREFE
Keyword(s):  
Mathematical Model ◽  
Ebola Virus ◽  
Virus Disease ◽  
Mass Action ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Protection Measures ◽  
Globally Asymptotically Stable ◽  
New Formulation ◽  
Self Protection

A mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42–74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number [Formula: see text] is less than or equal to unity and unstable when [Formula: see text]. In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid.

scholarly journals A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment

2020 ◽  
Vol 24 (5) ◽  
pp. 917-922
Author(s):  
J. Andrawus ◽  
F.Y. Eguda ◽  
I.G. Usman ◽  
S.I. Maiwa ◽  
I.M. Dibal ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Line Treatment ◽  
Second Line ◽  
Tuberculosis Transmission ◽  
Disease Free

This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results. Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point

A Mathematical Model for the Transmission Dynamics of Lymphatic Filariasis with Intervention Strategies

2019 ◽  
Vol 68 (3) ◽  
pp. 297-320
Author(s):  
S. M. Simelane ◽  
P. M. Mwamtobe ◽  
S. Abelman ◽  
J. M. Tchuenche
Keyword(s):  
Mathematical Model ◽  
Lymphatic Filariasis ◽  
Intervention Strategies ◽  
Transmission Dynamics
Sign in / Sign up

Export Citation Format

Share Document