scholarly journals Analisis Kestabilan Model Matematika Penyebaran Penyakit Schistosomiasis dengan Saturated Incidence Rate

2020 ◽  
Vol 2 (2) ◽  
pp. 71
Author(s):  
Elda Widya ◽  
Miswanto Miswanto ◽  
Cicik Alfiniyah
Keyword(s):  
Equilibrium Point ◽  
Incidence Rate ◽  
Infected Snail ◽  
Equilibrium Points ◽  
Incidence Rates ◽  
Endemic Equilibrium ◽  
Human Populations ◽  
Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

Schistosomiasis is a disease caused by infections of the genus Schistosoma. Schistosomiasis can be transmitted through schistosoma worms that contact human skin. Schistosomiasis is a disease that continues to increase in spread. Saturated incidence rates pay attention to the ability to infect a disease that is limited by an increase in the infected population. This thesis formulates and analyzes a mathematical model of the distribution of schistosomiasis with a saturated incidence rate. Based on the analysis of the model, two equilibrium points are obtained, namely non-endemic equilibrium points (E0) and endemic equilibrium points (E1). Both equilibrium points are conditional asymptotically stable. The nonendemic equilibrium point will be asymptotically stable if rh > dh, rs > ds and R0 < 1, while the endemic equilibrium point will be asymptotically stable if R0 > 1. Sensitivity analysis shows that there are parameters that affect the spread of the disease. Based on numerical simulation results show that when R0 < 1, the number of infected human populations (Hi), the number of infected snail populations (Si), the amount of cercaria density (C) and the amount of miracidia density (M) will tend to decrease until finally extinct. Otherwise at the time R0 > 1, the number of the four populations tends to increase before finally being in a constant state.

scholarly journals Mathematical Analysis of a Fractional-order "SIR" Epidemic Model with a General Nonlinear Saturated Incidence Rate in a Chemostat

2019 ◽  
pp. 1-12
Author(s):  
Miled El Hajji
Keyword(s):  
Incidence Rate ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Continuous Reactor ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

In the present work, a fractional-order differential equation based on the Susceptible-Infected- Recovered (SIR) model with nonlinear incidence rate in a continuous reactor is proposed. A profound qualitative analysis is given. The analysis of the local and global stability of equilibrium points is carried out. It is proved that if the basic reproduction number R > 1 then the disease-persistence (endemic) equilibrium is globally asymptotically stable. However, if R ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Finally, some numerical tests are done in order to validate the obtained results.

scholarly journals Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function

2021 ◽  
Vol 3 (2) ◽  
pp. 101-113
Author(s):  
Amit Kumar Chakraborty ◽  
M. A. Haque ◽  
M. A. Islam
Keyword(s):  
Incidence Rate ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Human Populations ◽  
Vector Population ◽  
Sirs Model ◽  
Treatment Function ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability

Dengue is one of the major health problems in Bangladesh and many people are died in recent years due to the severity of this disease. Therefore, in this paper, a SIRS model for the human and SI model for vector population with saturated incidence rate and constant treatment function has been presented to describe the transmission of dengue. The equilibrium points and the basic reproduction number have been computed. The conditions which lead the disease free equilibrium and the endemic equilibrium have been determined. The local stability for the equilibrium points has been established based on the eigenvalues of the Jacobian matrix and the global stability has been analyzed by using the Lyapunov function theory. It is found that the stability of equilibrium points can be controlled by the reproduction number. In order to calculate the infection rate, data for infected human populations have been collected from several health institutions of Bangladesh. Numerical simulations of various compartments have been generated using MATLAB to investigate the influence of the key parameters for the transmission of the disease and to support the analytical results. The effect of treatment function over the infected compartment has been illustrated. The sensitivity of the reproduction number concerning the parameters of the model has been analyzed. Finally, the most sensitive parameter that has the highest effect over reproduction number has been identified.

scholarly journals Asymptotic profile of endemic equilibrium to a diffusive epidemic model with saturated incidence rate

2019 ◽  
Vol 16 (5) ◽  
pp. 3885-3913 ◽  
Author(s):  
Yan’e Wang ◽  
◽  
Zhiguo Wang ◽  
Chengxia Lei ◽  
◽  
...  
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Asymptotic Profile ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate

2016 ◽  
Vol 09 (05) ◽  
pp. 1650068 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Yasir Khan ◽  
Sehra Khan ◽  
Saeed Islam
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free ◽  
The Basic Reproduction Number

This study considers SEIVR epidemic model with generalized nonlinear saturated incidence rate in the host population horizontally to estimate local and global equilibriums. By using the Routh–Hurwitz criteria, it is shown that if the basic reproduction number [Formula: see text], the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if [Formula: see text]. The geometric approach is used to present the global stability of the endemic equilibrium. For [Formula: see text], the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

scholarly journals Stability Analysis of SEIL Tuberculosis Epidemic Model with Logistic Growth in Susceptible Compartment

2021 ◽  
Vol 16 ◽  
pp. 1-9
Author(s):  
Joko Harianto
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Tuberculosis Disease ◽  
Disease Free ◽  
The Basic Reproduction Number

This article discusses modifications to the SEIL model that involve logistical growth. This model is used to describe the dynamics of the spread of tuberculosis disease in the population. The existence of the model's equilibrium points and its local stability depends on the basic reproduction number. If the basic reproduction number is less than unity, then there is one equilibrium point that is locally asymptotically stable. The equilibrium point is a disease-free equilibrium point. If the basic reproduction number ranges from one to three, then there are two equilibrium points. The two equilibrium points are disease-free equilibrium and endemic equilibrium points. Furthermore, for this case, the endemic equilibrium point is locally asymptotically stable.

scholarly journals Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR

2019 ◽  
Vol 16 (1) ◽  
pp. 107
Author(s):  
Willyam Daniel Sihotang ◽  
Ceria Clara Simbolon ◽  
July Hartiny ◽  
Desrinawati Tindaon ◽  
Lasker Pangarapan Sinaga
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Seir Model ◽  
Rate Of Spread ◽  
The Stability ◽  
Disease Free

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.

scholarly journals Stability Analysis of Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment

2020 ◽  
Vol 17 (1) ◽  
pp. 71-81
Author(s):  
Sulma Sulma ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Vaccination Campaign ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Infected People ◽  
The Stability ◽  
Vaccination Campaigns ◽  
The Mathematical Model

Meningitis is an infectious disease caused by bacteria, viruses, and protosoa and has the potential to cause an outbreak. Vaccination and campaign are carried out as an effort to prevent the spread of meningitis, treatment reduces the number of deaths caused by the disease and the number of infected people. This study aims to analyze and determine the stability of equilibrium point of the mathematical model of the spread of meningitis using five compartments namely susceptibles, carriers, infected without symptoms, infected with symptoms, and recovered with the effect of vaccination, campaign, and treatment. The results obtained from the analysis of the model that there are two equilibrium points, namely non endemic and endemic equilibrium points. If a certain condition is met then the non endemic equilibrium point will be asymptotically stable. Numerical simulations show that the spread of disease decreases with the influence of vaccination, campaign, and treatment.

scholarly journals Stability analysis in a delayed SIR epidemic model with a saturated incidence rate

2010 ◽  
Vol 15 (3) ◽  
pp. 299-306 ◽  
Author(s):  
A. Kaddar
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Basic Reproduction Number

We formulate a delayed SIR epidemic model by introducing a latent period into susceptible, and infectious individuals in incidence rate. This new reformulation provides a reasonable role of incubation period on the dynamics of SIR epidemic model. We show that if the basic reproduction number, denoted, R0, is less than unity, the diseasefree equilibrium is locally asymptotically stable. Moreover, we prove that if R0 > 1, the endemic equilibrium is locally asymptotically stable. In the end some numerical simulations are given to compare our model with existing model.

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