MULTISTABILITY AND SUBTHRESHOLD ENDEMIC STATES IN A MODEL FOR THE DYNAMICS OF NONSTERILIZING HIV VACCINES

2008 ◽  
Vol 18 (06) ◽  
pp. 1741-1748
Author(s):  
JORGE X. VELASCO-HERNÁNDEZ ◽  
BRENDA TAPIA-SANTOS
Keyword(s):  
Mathematical Model ◽  
Viral Load ◽  
Equilibrium Point ◽  
Application Rate ◽  
Endemic Equilibrium ◽  
Vaccination Policy ◽  
Hiv Vaccines ◽  
Infected People ◽  
Escape Mutants

A mathematical model for a nonsterilizing vaccine is studied. The model considers a vaccination policy represented by the vaccine application rate, waning and an index of reduction of viral load. The model also incorporates the possibility of escape mutants that avoid vaccine action. The main result is that we can show the existence of an endemic equilibrium point when R0 is less than one. The reason behind it is the existence of escape mutants that promote an increased rate of infection large enough to trigger an increase in the density of infected people even in the subthreshold case.

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

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

scholarly journals Lockdowns exert selection pressure on overdispersion of SARS-CoV-2 variants

2021 ◽  
Author(s):  
Bjarke Frost Nielsen ◽  
Andreas Eilersen ◽  
Lone Simonsen ◽  
Kim Sneppen
Keyword(s):  
Mathematical Model ◽  
Viral Load ◽  
Competitive Advantage ◽  
Selection Pressure ◽  
Transmission Risk ◽  
Social Contacts ◽  
Social Distancing ◽  
Infected People ◽  
Ancestral Strain

The SARS-CoV-2 ancestral strain has caused pronounced superspreading events, reflecting a disease characterized by overdispersion, where about 10% of infected people causes 80% of infections. New variants of the disease have different person-to-person variations in viral load, suggesting for example that the Alpha (B.1.1.7) variant is more infectious but relatively less prone to superspreading. Meanwhile, mitigation of the pandemic has focused on limiting social contacts (lockdowns, regulations on gatherings) and decreasing transmission risk through mask wearing and social distancing. Using a mathematical model, we show that the competitive advantage of disease variants may heavily depend on the restrictions imposed. In particular, we find that lockdowns exert an evolutionary pressure which favours variants with lower levels of overdispersion. We find that overdispersion is an evolutionarily unstable trait, with a tendency for more homogeneously spreading variants to eventually dominate.

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 Qualitative analysis of a mathematical model of divorce epidemic with anti-divorce therapy

2021 ◽  
Vol 4 (2) ◽  
pp. 1-11
Author(s):  
Reuben Iortyer Gweryina ◽  
◽  
Francis Shienbee Kaduna ◽  
Muhammadu Yahaya Kura ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Qualitative Analysis ◽  
Equilibrium Point ◽  
Lyapunov Functions ◽  
Family System ◽  
Endemic Equilibrium ◽  
Epidemiological Model ◽  
Living Together ◽  
Stable Family ◽  
Globally Stable

Marriage is the living together of two persons as husband and wife. Separation and Divorce are the frontier challenges facing the existence of stable family system. In this paper, we construct an epidemiological model of divorce epidemic using standard incidence function as force of marital disunity. The study examines qualitatively that the two equilibra (divorce-free and endemic equilibrium point) are globally stable by Lyapunov functions. Numerical results reveal that, anti-divorce protocols and reconciliation can jointly stabilize marriages, and Married cases that survive divorce epidemic in 30 years period of marriage (twice the survival period of separation) cannot break again.

scholarly journals SEIPR-Mathematical Model of the Pneumonia Spreading in Toddlers with Immunization and Treatment Effects

2020 ◽  
Vol 17 (2) ◽  
pp. 202-218
Author(s):  
Rusniwati S. Imran ◽  
Resmawan Resmawan ◽  
Novianita Achmad ◽  
Agusyarif Rezka Nuha
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Treatment Success ◽  
Stable State ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Disease Spread ◽  
Reproductive Number

This research discussed the SEIPR mathematical model on the spread of pneumonia among children under five years old. The development of the model was done by considering factors of immunization and treatment factors, in an effort to reduce the rate of spread of pneumonia. In this research, mathematical model construction, stability analysis, and numerical simulation were carried out to see the dynamics of pneumonia cases in the population. The model analysis produces two equilibrium points, which are the equilibrium point without the disease, the endemic equilibrium point, and the basic reproduction number ( ) as the threshold value for disease spread. The point of equilibrium without disease reaches a stable state at the moment , which indicates that pneumonia will disappear from the population, while the endemic equilibrium point reaches a stable state at that time , which indicates that the disease will spread in the population. Furthermore, numerical simulations show that increasing the rate parameters of infected individuals undergoing treatment ( ), the treatment success rate ( ), and the immunization proportion ( ), could suppress the basic reproductive number so that control of the disease spread rate can be accelerated.

scholarly journals Model matematika SMEIUR pada penyebaran penyakit campak dengan faktor pengobatan

2020 ◽  
Vol 1 (2) ◽  
pp. 71-80
Author(s):  
Anisa Fitra Dila Hubu ◽  
Novianita Achmad ◽  
Nurwan Nurwan
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Health Sector ◽  
Endemic Equilibrium ◽  
Exposed Population ◽  
The Stability ◽  
Parameter Values ◽  
Disease Free

This study discusses the spread of measles in a mathematical model. Mathematical modeling is not only limited to the world of mathematics but can also be applied in the health sector. Measles is a disease with a high transmission rate. The spread of measles in this model was modified by adding the treated population and the treatment parameters of the exposed population. In this article, we examine the equilibrium points in the SMEIUR mathematical model and perform stability analysis and numerical simulations. In this study, two equilibrium points were obtained, namely the disease-free and endemic equilibrium point. After getting the equilibrium point, an analysis is carried out to find the stability of the model. Furthermore, the simulation produces a stable disease-free equilibrium point at conditions R01 and a stable endemic equilibrium point at conditions R01. In this study, a numerical simulation was carried out to see population dynamics by varying the parameter values. The simulation results show that to reduce the spread of measles, it is necessary to increase the rate of advanced immunization, the rate of the infected population undergoing treatment, and the proportion of individuals who are treated cured.

scholarly journals MSEICR Fractional Order Mathematical Model of The Spread Hepatitis B

2020 ◽  
Vol 17 (2) ◽  
pp. 314-324
Author(s):  
Suriani Suriani ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Mathematical Model ◽  
Hepatitis B ◽  
Qualitative Methods ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Jacobian Matrix ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Fractional Orders

This research aims to develop the MSEICR model by reviewing fractional orders on the spread of Hepatitis B by administering vaccinations and treatment, and analyzing fractional effects by numerical simulations of the MSEICR mathematical model using the method Grunwald Letnikov. Researchers use qualitative methods to achieve the object of research. The steps are to determine the MSEICR model by reviewing the fractional order, looking for endemic equilibrium points for each non-endemic and endemic equilibrium point, determining the equality of characteristics and eigenvalues ​​of the Jacobian matrix. Next, look for values  ​​(Basic Reproductive Numbers), analyze stability around non-endemic and endemic equilibrium points and complete numerical simulations. From the simulation provided, it is known that by giving a fractional alpha value of and  , the greater the value of the fractional order parameters used, the movement of the solution graphs is getting closer to the equilibrium point. If given and still endemic, whereas if and  the value  is increased to non-endemic, then the number of hepatitis B sufferers will disappear.

scholarly journals Qualitative properties of mathematical model of English language education

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Atena Ghasemabadi ◽  
Nahid Soltanian
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Equilibrium Point ◽  
English Language ◽  
Language Education ◽  
Qualitative Properties ◽  
English Language Education ◽  
Compound Matrices ◽  
Reproduction Numbers ◽  
Coexistence Equilibrium

AbstractThis paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that backward bifurcation occurs. In addition, we investigate the existence and local and global stability of boundary equilibria and coexistence equilibrium point and the global stability of the coexistence equilibrium point using compound matrices.

Sign in / Sign up

Export Citation Format

Share Document