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 Sensitivity and mathematical model analysis on secondhand smoking tobacco

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Birliew Fekede ◽  
Benyam Mebrate
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Reproductive Number ◽  
Primary Case ◽  
Susceptible Population ◽  
Proposed Model ◽  
Relative Change ◽  
Well Posed ◽  
Mathematical Model Analysis

AbstractIn this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If $$R_{0}<1,$$ R 0 < 1 , the smoking-free equilibrium point is stable, and if $$R_{0}>1,$$ R 0 > 1 , endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in $$R_{0}$$ R 0 when the value of the parameter changes.

Boundedness and Stability Properties of Solutions of Mathematical Model of Measles.

2021 ◽  
Vol 52 (1) ◽  
pp. 91-112
Author(s):  
Babatunde Sunday Ogundare ◽  
James Akingbade
Keyword(s):  
Mathematical Model ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Jacobian Determinant ◽  
Stability Of Solutions ◽  
Open Population ◽  
Disease Free

In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number $R_0$ was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population.

scholarly journals Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Ebrima Kanyi ◽  
Ayodeji Sunday Afolabi ◽  
Nelson Owuor Onyango
Keyword(s):  
Equilibrium Point ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Modeling And Analysis ◽  
Disease Free

This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R 0 , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R 0 > 1 . It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R 0 < 1 , and the unique endemic equilibrium point is locally asymptotically stable whenever R 0 > 1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R 0 = 1 , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R 0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis.

scholarly journals Modelling the effect of vertical transmission in the dynamics of HIV/AIDS in an age-structured population

2003 ◽  
Vol 21 (1) ◽  
pp. 82 ◽  
Author(s):  
J. Y. T. Mugisha ◽  
L. S. Luboobi
Keyword(s):  
Vertical Transmission ◽  
Equilibrium Points ◽  
Age Groups ◽  
Endemic Equilibrium ◽  
Mass Action ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
First Case ◽  
Age Structured ◽  
Hiv Aids

We use a continuous age-structured model of McKendrick-von-Foerster type to derive a two-age groups HIV/AIDS epidemic model. In the analysis of the model, keen interest is put on the role of vertical transmission in the dynamics of the spread of the epidemic. The model is analysed in two scenarios: the case when the force of infection is a constant and the case when we have it as a mass action. In the first case, the only possible equilibrium is the endemic equilibrium. In this situation, we show that if all babies born to infected mothers are HIV-free we have the basic reproductive number R0 = 0 and as such the epidemic will die out. In the second case, we show that both the disease-free and endemic equilibrium points exist. We also derive conditions for their stability.

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 Modelling and Simulating a Transmission of COVID-19 Disease: Niger Republic Case

2020 ◽  
Vol 13 (3) ◽  
pp. 549-566
Author(s):  
Abba Mahamane Oumarou ◽  
Saley Bisso
Keyword(s):  
Matrix Method ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Contact Rate ◽  
Asymptotically Stable ◽  
Next Generation Matrix ◽  
The Impact ◽  
Disease Free

This paper focuses on the dynamics of spreads of a coronavirus disease (Covid-19).Through this paper, we study the impact of a contact rate in the transmission of the disease. We determine the basic reproductive number R0, by using the next generation matrix method. We also determine the Disease Free Equilibrium and Endemic Equilibrium points of our model. We prove that the Disease Free Equilibrium is asymptotically stable if R0 < 1 and unstable if R0 > 1. The asymptotical stability of Endemic Equilibrium is also establish. Numerical simulations are made to show the impact of contact rate in the spread of disease.

scholarly journals Stability Analysis of the Corruption Free Equilibrium of the Mathematical Model of Corruption in Nigeria

2020 ◽  
Vol 8 (2) ◽  
pp. 61-68
Author(s):  
Victor Akinsola ◽  
ADEYEMI BINUYO
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Equilibrium State ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Operator Technique ◽  
Eigen Values ◽  
The Stability ◽  
The Mathematical Model

In this paper, a mathematical model of the transmission dynamics of corruption among populace is analyzed. The corruption free equilibrium state, characteristic equation and Eigen values of the corruption model were obtained. The basic reproductive number of the corruption model was also determined using the next generation operator technique at the corruption free equilibrium points. The condition for the stability of the corruption free equilibrium state was determined. The local stability analysis of the mathematical model of corruption was done and the results were presented and discussed accordingly. Recommendations were made from the results on measures to reduce the rate of corrupt practices among the populace.   

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.

Modeling and stability analysis of the spread of novel coronavirus disease COVID-19

2021 ◽  
pp. 2150035
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
D. Abraham Vianny ◽  
Mary Jacintha ◽  
Fatma Bozkurt Yousef
Keyword(s):  
Fractional Order ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Basic Reproductive Number ◽  
Phase Portraits ◽  
Transmission Model ◽  
Reproductive Number ◽  
Discrete Version ◽  
Novel Coronavirus

Towards the end of 2019, the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain of coronavirus that was unidentified in humans previously. In this paper, a new fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where the population is infected due to human transmission. The fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix approach. All equilibrium points related to the disease transmission model are then computed. Further, sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number (local stability) and are supported with time series, phase portraits and bifurcation diagrams. Finally, numerical simulations are provided to demonstrate the theoretical findings.

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