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Journal articles on the topic 'Endemic equilibrium point (EEP)'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Peter, Cheruiyot Kibii, Kirui Wesley, Langat Reuben, and Tonui Benard. "Modelling the Effects of Vaccination and Incubation on Covid-19 Transmission Dynamics." Journal of Advances in Mathematics and Computer Science 40, no. 7 (2025): 1–12. https://doi.org/10.9734/jamcs/2025/v40i72017.

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The Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-COV-2) is a strain of Coronavirus that causes Coronavirus Disease 2019 (COVID-19). The respiratory illness responsible for the COVID19 pandemic began in December 2019 in Wuhan city, China. Mathematical modeling has enabled the epidemiologist to understand the dynamics of the disease, its impact and future predictions in order to provide the governments with the best policies and strategies to curb the spread of the virus. Deterministic susceptible-vaccinated-asymptomatic-infectious-recovered (SVAIR) model was formulated incorporated wit

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2

Sulayman, Fatima, and Farah Aini Abdullah. "Dynamical Behaviour of a Modified Tuberculosis Model with Impact of Public Health Education and Hospital Treatment." Axioms 11, no. 12 (2022): 723. http://dx.doi.org/10.3390/axioms11120723.

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Tuberculosis (TB), caused by Mycobacterium tuberculosis is one of the treacherous infectious diseases of global concern. In this paper, we consider a deterministic model of TB infection with the public health education and hospital treatment impact. The effective reproductive number, Rph, that measures the potential spread of TB is presented by employing the next generation matrix approach. We investigate local and global stability of the TB-free equilibrium point, endemic equilibrium point, and sensitivity analysis. The analyses of the proposed model show that the model undergoes the phenomen

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3

Rotich, Titus, Robert Cheruiyot, Pauline Anupi, and Flomena Jeptanui. "Modeling metapopulation dynamics of HIV epidemic on a linear lattice with nearest neighbour coupling." International Journal of Applied Mathematical Research 5, no. 1 (2016): 73. http://dx.doi.org/10.14419/ijamr.v5i1.5544.

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<p>Many mathematical models for the spread of infectious diseases in a population assume homogeneous mixing, but due to spatial distribution, there exist distinct patches with unique disease dispersion dynamics, especially if between patch mixing due to travel and migration is limited. In this paper, three levels of disease status in a - patch metapopulation was studied using a simple SIR-HIV epidemic model in a one dimensional nearest neighbour coupling lattice. The basic reproductive ratio , which is a function of coupling strength , is shown to affect stability characteristics of equi

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4

A., L. M. Murwayi, Onyango T., and Owour B. "Mathematical Analysis of Plant Disease Dispersion Model that Incorporates wind Strength and Insect Vector at Equilibrium." British Journal of Mathematics & Computer Science 22, no. 5 (2017): 1–17. https://doi.org/10.9734/BJMCS/2017/33991.

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Numerous plant diseases caused by pathogens like bacteria, viruses, fungi protozoa and pathogenic nematodes are propagated through media such as water, wind and other intermediary carries called vectors, and are therefore referred to as vector borne plant diseases. Insect vector borne plant diseases are currently a major concern due to abundance of insects in the tropics which impacts negatively on food security, human health and world economies. Elimination or control of which can be achieved through understanding the process of propagation via Mathematical modeling. However existing models a

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Egonmwan, A. O., and D. Okuonghae. "Mathematical analysis of a tuberculosis model with imperfect vaccine." International Journal of Biomathematics 12, no. 07 (2019): 1950073. http://dx.doi.org/10.1142/s1793524519500736.

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Since 1921, the Bacille Calmette–Guerin (BCG) vaccine continues to be the most widely used vaccine for the prevention of Tuberculosis (TB). However, the immunity induced by BCG wanes out after some time making the vaccinated individual susceptible to TB infection. In this work, we formulate a mathematical model that incorporates the vaccination of newly born children and older susceptible individuals in the transmission dynamics of TB in a population, with a vaccine that can confer protection on older susceptible individuals. In the absence of disease-induced deaths, the model is shown to unde

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6

Utomo, Rukmono Budi, and Azizah Azizah. "MATHEMATICS MODEL SIRS-SI OF TRANSMISSION DENGUE VIRUS CONSIDERING FUMIGATION, VACCINATION AND TREATMEN IN CASE OF TANGERANG CITY." Indonesian Journal of Applied Mathematics 4, no. 2 (2025): 47. https://doi.org/10.35472/indojam.v4i2.1913.

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Abstract: In this paper, we construct a mathematical model SIRS-SI transmission dengue fever considering fumigation, vaccination and treatment in case Tangerang City. Background why this research has to do because in Tangerang City the case of dengue fever is pretty lot. Method in this research is using compartment model and create differential equation system. We also do some analyze the model like determining free disease equilibrium point and endemic equilibrium point. We also determining basic reproduction number and making analyze stability of the model around equilibrium points. We also

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7

Andrawus, J., F. Y. Eguda, I. G. Usman, et al. "A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment." Journal of Applied Sciences and Environmental Management 24, no. 5 (2020): 917–22. http://dx.doi.org/10.4314/jasem.v24i5.29.

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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.

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Ginting, Rini Sania br, and Yudi Ari Adi. "A mathematical model of meningitis with antibiotic effects." Bulletin of Applied Mathematics and Mathematics Education 3, no. 1 (2023): 1–14. http://dx.doi.org/10.12928/bamme.v3i1.9475.

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The mathematical model in this study is a SCIR-type meningitis disease spread model, namely susceptible (S), carrier (C), infected (I), and recovery (R). In the model used, there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The conditions and stability of the equilibrium point are determined by the basic reproduction number, which is the value that determines whether or not the spread of meningitis infection in a population. The results of this study show that the stability of the disease-free equilibrium point and the endemic equilib

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9

Rois, Muhammad Abdurrahman, Mohamad Tafrikan, Yolanda Norasia, Indira Anggriani, and Mohammad Ghani. "SEIHR Model on Spread of COVID-19 and Its Simulation." Telematika 15, no. 2 (2022): 70–80. http://dx.doi.org/10.35671/telematika.v15i2.1141.

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The modified SEIR model of the COVID-19 spread is divided into five compartments: susceptible, exposed, infected, and recovered. Based on the results, two equilibrium points were obtained: the disease-free equilibrium point and the endemic equilibrium point. The existence of an equilibrium point depends on the value of the basic reproduction number R0, as well as on stability. The endemic equilibrium point exists if it is satisfied R0>1. Then, the disease-free equilibrium point is said to be locally asymptotic stable if R0<1, and the endemic equilibrium point is locally asymptotic stable

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Pagalay, Usman, Juhari, and Sindi Ayuna Hustani. "Dynamic Analysis of a Mathematical Model of the Anti-Tumor Immune Response." ITM Web of Conferences 58 (2024): 01008. http://dx.doi.org/10.1051/itmconf/20245801008.

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This study discusses the dynamic analysis, the Hopf bifurcation, and numerical simulations. The mathematical model of the anti-tumor immune response consists of three compartments namely Immature T Lymphocytes (L1), Mature T Lymphocytes (L2) and Tumor Cells (T). This research was conducted to represent the behavior between immune cells and tumor cells in the body with five γ conditions. Where γ is the intrinsic growth rate of mature T lymphocytes. This study produces R0 > 1 in conditions 1 to 4 while in condition 5 produces R0 < 1. The disease-free equilibrium point is stable only in con

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11

Miswanto, Nisrina Firsta Ammara, and Windarto. "Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Leptospirosis dengan Saturated Incidence Rate." Contemporary Mathematics and Applications (ConMathA) 5, no. 2 (2023): 102–21. http://dx.doi.org/10.20473/conmatha.v5i2.49379.

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Leptospirosis is a disease caused by the bacteria Leptospira inchterohemorrhagiaea. Leptospirosis can attack humans and other animals, through rodents, especially rats. This research aims to analyze the stability of the equilibrium point in the mathematical model of the spread of Leptospirosis and apply optimal control variables in the form of prevention and treatment efforts. Based on the results of the mathematical model analysis of the spread of Leptospirosis, two equilibrium points were obtained, there are the non-endemic equilibrium point and the endemic equilibrium point. Local stability

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Anwar, Abdul Faliq, Windarto Windarto, and Cicik Alfiniyah. "Analisis Kestabilan Model Matematika Ko-infeksi Virus Influenza A dan Pneumokokus pada Sel Inang." Contemporary Mathematics and Applications (ConMathA) 1, no. 2 (2020): 74. http://dx.doi.org/10.20473/conmatha.v1i2.17385.

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Co-infection of influenza A virus and pneumococcus is caused by influenza A virus and pneumococcus bacteria which infected host cell at the same time. The purpose of this thesis is to analyze stability of equilibrium point on mathematical model within-host co-infection of influenza A and pneumococcus. Based on anlytical result of the model there are four quilibrium points, non endemic co-infection equilibrium (E0), endemic influenza A virus equilibrium (E1), endemic pneumococcus equilbrium (E2) and endemic co-infection equilibrium (E3). By Next Generation Matrix (NGM), we obtain two basic repr

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13

Harianto, Joko, and Titik Suparwati. "SVIR Epidemic Model with Non Constant Population." CAUCHY 5, no. 3 (2018): 102. http://dx.doi.org/10.18860/ca.v5i3.5511.

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In this article, we present an SVIR epidemic model with deadly deseases and non constant population. We only discuss the local stability analysis of the model. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium point. The local stability of the disease free and endemic equilibrium exists when the basic reproduction number less or greater than unity, respectively. If the value of R0 less than one then the desease free equilibrium point is locally asymptotically stable, and if its exceeds, the endemic equil

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14

DAS, PRASENJIT, DEBASIS MUKHERJEE, and A. K. SARKAR. "STUDY OF A CARRIER DEPENDENT INFECTIOUS DISEASE — CHOLERA." Journal of Biological Systems 13, no. 03 (2005): 233–44. http://dx.doi.org/10.1142/s0218339005001495.

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This paper analyzes an epidemic model for carrier dependent infectious disease — cholera. Existence criteria of carrier-free equilibrium point and endemic equilibrium point (unique or multiple) are discussed. Some threshold conditions are derived for which disease-free, carrier-free as well as endemic equilibrium become locally stable. Further global stability criteria of the carrier-free equilibrium and endemic equilibrium are achieved. Conditions for survival of all populations are also determined. Lastly numerical simulations are performed to validate the results obtained.

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15

Subahtul, Nurul, and Toto Nusantara. "ANALISIS KESTABILAN MODEL EPIDEMI SEIVR PADA PENYAKIT HEPATITIS B." Jurnal Kajian Matematika dan Aplikasinya (JKMA) 1, no. 1 (2020): 27. http://dx.doi.org/10.17977/um055v1i12020p27-32.

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In this study, the SEIVR epidemic model was used to analyze the stability of the spread Hepatitis B based on data obtained from the 2016 RI Health Data of East Java Province. In analyzing the model there are several procedures used, namely find the equilibrium point, analyzing the stability of the equilibrium point, find the basic reproduction number (R_0), and the last one doing the simulation based on the data obtained using the Maple17 program. Based on the research that has been done, two equilibrium points are obtained, namely the disease-free equilibrium point and endemic equilibrium poi

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KT, Ummul Aulia, Heni Widayani, and Ari Kusumastuti. "Analisis Dinamik Model Infeksi Mikrobakterium Tuberkulosis Dengan Dua Lokasi Pengobatan." Jurnal Riset Mahasiswa Matematika 2, no. 3 (2023): 113–21. http://dx.doi.org/10.18860/jrmm.v2i3.16753.

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Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. The disease is considered dangerous because it infects the lungs and other organs of the body and can lead to death. This study discusses a mathematical model for the spread of tuberculosis with two treatment sites as an effort to reduce the transmission rate of TB cases. Treatment for TB patients can be done at home and in hospitals. The purpose of this study was to construct a mathematical model and analyze the qualitative behavior of the TB spread model. The construction of the model uses the SEIR epidemic model whi

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17

Putri, Nurul Qorima, and Paian Sianturi. "ANALISIS DINAMIKA PENYEBARAN COVID-19 DENGAN LAJU INSIDEN NONLINEAR." MES: Journal of Mathematics Education and Science 6, no. 2 (2021): 9–32. http://dx.doi.org/10.30743/mes.v6i2.3358.

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This research is focused on discussing the SEIQRS epidemic model for the spread of the COVID-19 disease with a nonlinear incidence rate. From the result of analysis of the SEIQR model obtained two equilibrium point these are diseases free equilibrium points and endemic equilibrium point. Then, the analysis of the completion behavior is done by using eigenvalues and stability around equilibrium point, the obtained result of the diseases free equilibrium point has two stability traits are saddle point, and stable. The stability diseases free equilibrium will be stable when R0 1, if R0 1 then the

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18

Zheng, Lifei, Xiuxiang Yang, and Liang Zhang. "On global stability analysis for SEIRS models in epidemiology with nonlinear incidence rate function." International Journal of Biomathematics 10, no. 02 (2017): 1750019. http://dx.doi.org/10.1142/s179352451750019x.

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We study an SEIRS epidemic model with an isolation and nonlinear incidence rate function. We have obtained a threshold value [Formula: see text] and shown that there is only a disease-free equilibrium point, when [Formula: see text] and an endemic equilibrium point if [Formula: see text]. We have shown that both disease-free and endemic equilibrium point are globally stable.

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19

Harianto, Joko. "Stability Analysis of SEIL Tuberculosis Epidemic Model with Logistic Growth in Susceptible Compartment." ASM Science Journal 16 (December 22, 2021): 1–9. http://dx.doi.org/10.32802/asmscj.2021.733.

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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 equil

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20

Wang, Xinhe, Zhen Wang, Xia Huang, and Yuxia Li. "Dynamic Analysis of a Delayed Fractional-Order SIR Model with Saturated Incidence and Treatment Functions." International Journal of Bifurcation and Chaos 28, no. 14 (2018): 1850180. http://dx.doi.org/10.1142/s0218127418501808.

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In this paper, a delayed fractional-order SIR (susceptible, infected, and removed) epidemic model with saturated incidence and treatment functions is presented. Firstly, the non-negativity and boundedness of solutions of the proposed model are proved. Next, some sufficient conditions are established to ensure the local asymptotic stability of the disease-free equilibrium point [Formula: see text] and the endemic equilibrium point [Formula: see text] for any delay. Meanwhile, global asymptotic stability of the endemic equilibrium point [Formula: see text] is investigated by constructing a suita

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21

Sitinjak, Novandri, and Tri Andri Hutapea. "Stability Analysis of Mathematical Models of Toxoplasmosis Spread in Cat and Human Populations with Time Delay." Formosa Journal of Science and Technology 2, no. 2 (2023): 433–52. http://dx.doi.org/10.55927/fjst.v2i2.2855.

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Toxoplasmosis is caused by the parasite Toxoplasma gondii. In this study, model construction, determining the equilibrium point, stability analysis, and model simulation were carried out. The results showed that there were two equilibrium points, namely the disease-free equilibrium point, locally asymptotically stable if and disease endemic, locally asymptotically stable if. The simulation results show when the solution is stable towards the free equilibrium point, when the solution is stable towards the disease endemic equilibrium point without delay or with time delay. Giving a time delay wi

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Lailatuz Arromadhani and Budi Priyo Prawoto. "Stability Analysis of Monkeypox Transmission Model by Administering Vaccine." Numerical: Jurnal Matematika dan Pendidikan Matematika 7, no. 1 (2023): 195–210. http://dx.doi.org/10.25217/numerical.v7i1.3481.

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Monkeypox is an infectious disease that affects mammals, including humans and some primates. Monkeypox transmission can be prevented by administering vaccinations to the human population. This study aims to construct and analyze the monkeypox transmission model's stability with vaccination. There are six sub-populations: Vaccinated humans ( ), Susceptible humans ( ), Infected human , Recovered human , Susceptible animal , and Infected human . Several steps are literature study, formulating assumptions, constructing models, finding equilibrium points, searching for reproduction numbers by next-

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Adi, Y. A., N. Irsalinda, A. Wiraya, S. Sugiyarto, and Z. A. Rafsanjani. "An epidemic model with viral mutations and vaccine interventions." Mathematical Modeling and Computing 10, no. 2 (2023): 311–25. http://dx.doi.org/10.23939/mmc2023.02.311.

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In this paper, we introduce a two-strain SIR epidemic model with viral mutation and vaccine administration. We discuss and analyze the existence and stability of equilibrium points. This model has three types of equilibrium points, namely disease-free equilibrium, dominance equilibrium point of strain two, and coexistence endemic equilibrium point. The local stability of the dominance equilibrium point of strain two and coexistence endemic equilibrium point are verified by using the Routh--Hurwitz criteria, while for the global stability of the dominance equilibrium point of strain two, we use

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Eli, Innocent Cleopas. "Mathematical Modelling of the Epidemiology of Tuberculosis with Silicosis Coinfection." International Journal of Research and Innovation in Applied Science X, no. II (2025): 603–24. https://doi.org/10.51584/ijrias.2025.10020051.

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The study presents an innovative mathematical model analysing the epidemiology of Tuberculosis with silicosis coinfection. It effectively integrates epidemiological factors and historical theoretical research with well-structured model formulation and numerical verification through MATLAB. The use of partial differential equation, Jacobian matrix, deterministic techniques as well as Routh Hurwitz algebraic criteria plays significant role in the stability of disease-free equilibrium point and stability of the endemic equilibrium point analytically which indicates locally stable system asymptoti

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Alkali, M., Musa Abdullahi, A. Alhassan, S. Muhammad, and H. Zailani. "MATHEMATICAL ANALYSIS OF A RISK STRUCTURED LISTERIOSIS DYNAMICS MODEL." FUDMA JOURNAL OF SCIENCES 9, no. 3 (2025): 302–8. https://doi.org/10.33003/fjs-2025-0903-3259.

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A foodborne disease called listeriosis is brought on by the bacteria Listeria monocytogenes which typically infects people after consuming contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, we developed and analyzed a risk-structured mathematical model describing the dynamics of Listeriosis using ordinary differential equations. Three equilibrium points were obtained, viz; disease free equilibrium point, , bacteria free equilibrium point, , and endemic equilibrium point, . Contaminated food threshold was established as

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(Alm), Jafaruddin, Rapmaida M. Pangaribuan, Aryanto, and Irena A. Henukh. "Analisis Kestabilan Model Host-Vector Transmisi HIV/AIDS Pada Pengguna Jarum Suntik." Jurnal Matematika 7, no. 1 (2017): 1. http://dx.doi.org/10.24843/jmat.2017.v07.i01.p77.

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HIV/AIDS is a very dangerous disease. The transmission of HIV/AIDS can be in three ways and one of them through a syringe. In this paper we describe SIR and SEIR Host-Vector model transmission of HIV/AIDS amongst populations of injecting drug users. From the existing model we obtained disease-free equilibrium point and endemic equilibrium point. Then we study the stability conditions and sensitivity analysis of the . The analysis shows if then the disease-free equilibrium point is stable and if then the endemic equilibrium point will be stable. We also obtained that parameter of probality host

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Siddik, A. Muh Amil, Syamsuddin Toaha, and Andi Muhammad Anwar. "Stability Analysis of Prey-Predator Model With Holling Type IV Functional Response and Infectious Predator." Jurnal Matematika, Statistika dan Komputasi 17, no. 2 (2020): 155–65. http://dx.doi.org/10.20956/jmsk.v17i2.11716.

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Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except , that may exist and stable. Simulation results show that with the variation of several par

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Nurwijaya, Sugian, Ratnah Kurniati MA, and Sigit Sugiarto. "DYNAMICAL SYSTEM FOR EBOLA OUTBREAK WITHIN QUARANTINE AND VACCINATION TREATMENTS." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 2 (2023): 0615–24. http://dx.doi.org/10.30598/barekengvol17iss2pp0615-0624.

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Ebola Virus Disease (EVD) is an infectious disease with a high mortality rate which is caused by the virus from the family of Filoviridae, genus of Ebolavirus. Therefore, this research works on the developing model of Ebola disease spread with SLSHVEQIHR type. The purpose of this study is to analyze the spread of Ebola disease with the treatments, which are quarantine and vaccination. Then determine the equilibrium point and basic reproduction number (R0). There are two equilibrium points, the disease free equilibrium point and the endemic equilibrium point. The analysis results in the model s

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Suriani, Suriani, Syamsuddin Toaha, and Kasbawati Kasbawati. "MSEICR Fractional Order Mathematical Model of The Spread Hepatitis B." Jurnal Matematika, Statistika dan Komputasi 17, no. 2 (2020): 314–24. http://dx.doi.org/10.20956/jmsk.v17i2.10994.

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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 ma

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Harianto, Joko. "Local Stability Analysis of an SVIR Epidemic Model." CAUCHY 5, no. 1 (2017): 20. http://dx.doi.org/10.18860/ca.v5i1.4388.

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In this paper, we present an SVIR epidemic model with deadly deseases. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium. The local stability of the disease free and endemic equilibrium exists when the basic reproduction number less or greater than unity, respectively. If the value of R0 less than one then the desease free equilibrium is locally stable, and if its exceeds, the endemic equilibrium is locally stable. The numerical results are presented for illustration.

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Soleh, Mohammad, Mutia Nazvira, Wartono Wartono, Elfira Safitri, and Riry Sriningsih. "STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT." BAREKENG: Jurnal Ilmu Matematika dan Terapan 19, no. 1 (2025): 173–84. https://doi.org/10.30598/barekengvol19iss1pp173-184.

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Diphtheria is an acute disease that affects the upper respiratory tract caused by Corynebacterium diphtheriae, which can also affect the skin, eyes, and other organs. This article analyzes the stability of the SIQR model of diphtheria disease spread in Mandau District by considering the migration factor. The SIQR model is a development of the SIR model by incorporating the quarantine process as an alternative to reduce morbidity. The purpose of this study is to see the effect of migration on the spread of diphtheria disease in Mandau District through mathematical model simulation. We calculate

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Rahman, K. S., S. R. Mitkari, and S. Shaikh. "Modeling the Impact of Vaccination, Screening, Treatment on the Dynamics of Pneumonia." Journal of Scientific Research 12, no. 4 (2020): 525–36. http://dx.doi.org/10.3329/jsr.v12i4.45815.

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In this paper we have presented a deterministic model for pneumonia transmission and we have used the model to avail the potential impact of therapy. The model is based on the vaccinated-susceptible-carrier-infected-recovered-susceptible compartmental structure and their possible interventions with the possibility of infected individual recovery from natural immunity. Here, we have modeled Pneumonia considering vaccination, screening and treatment with a system of nonlinear ordinary differential equation. The model reproduction number R0 is derived and the stability of the equilibria are deriv

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Syafitri, Risyqaa, Trisilowati Trisilowati, and Wuryansari Muharini Kusumawinahyu. "Dynamics of Covid-19 model with public awareness, quarantine, and isolation." Jambura Journal of Biomathematics (JJBM) 4, no. 1 (2023): 63–68. http://dx.doi.org/10.34312/jjbm.v4i1.19832.

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This paper presents a new COVID-19 model that contains public awareness, quarantine, and isolation. The model includes eight compartments: susceptible aware (SA), susceptible unaware (SU), exposed (E), asymptomatic infected (A), symptomatic infected (I), recovered (R), quarantined (Q), and isolated (J). The introduction will be shown in the first section, followed by the model simulation. The equilibrium points, basic reproduction number, and stability of the equilibrium points are then determined. The model has two equilibrium points: disease-free equilibrium point and endemic equilibrium poi

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Asriyah, Desti, Norma Muhtar, and Arman. "MODEL MATEMATIKA PENYAKIT HEPATITIS B DENGAN PENGARUH TRANSMISI VERTIKAL." Jurnal Matematika Komputasi dan Statistika 4, no. 3 (2025): 813–19. https://doi.org/10.33772/jmks.v4i3.62.

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Hepatitis B is an infectious disease caused by a virus (HBV). This virus is one type of many viruses that attack the liver. This study aims to discuss the mathematical model of hepatitis B disease with the effect of vertical transmission. From the results of the analysis obtained two disease-free balance points and endemic balance points. Furthermore, an analysis of the behavior of the solution is carried out using the eigenvalues and the properties of stability at the equilibrium point, the result is that the disease-free equilibrium point has two stability properties, namely saddle point and

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Dr Arvind kumar yadav, Mamta Raipuriya,. "Transmission Dynamics of Measles: A Mathematical Model." International Journal of Scientific Research and Management (IJSRM) 5, no. 7 (2017): 6501–5. http://dx.doi.org/10.18535/ijsrm/v5i7.88.

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In this paper, a mathematical model has been studied the stability of the disease free and endemicequilibrium point and their linear stability analysis have been conducted. The model it has been shown that the disease free and also the endemic equilibrium point are linearly asymptotically stable. From the stability of disease free equilibrium point it can be shown, disease will not spread in the population and the endemic quilibrium point it can be conclude that disease will remain in the population.

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Sari, Erna, Asrul Sani, and Muh Kabil Djafar. "Analisis Model Epidemi Penyebaran Tuberkulosis Dengan Struktur Umur." JOSTECH Journal of Science and Technology 3, no. 2 (2023): 133–43. http://dx.doi.org/10.15548/jostech.v3i2.6064.

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Tuberculosis (TBC) is a contagious disease caused by infection with the bacterium Mycobacterium tuberculosis (Mtb), which attacks the lungs. taking into account the laten period of individuals infected with tuberculosis, this study uses the SEIRS model. The total population is grouped into two age groups, group child and group adult . The purpose of this research is to determine SEIRS model of the spread tuberculosis disease with age structure and its completion behavior. The steps in analyzing of the model can be done by determining the equilibrium point, the results are obtained two equilibr

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Amar, Muh Ikhsan, Muhammad Rifki Nisardi, and Muhammad Fadhil Nurahmad. "A Deterministic Mathematical Model of Meningitis Transmission Dynamics with Vaccination and Screening." Jurnal Matematika UNAND 14, no. 1 (2025): 14. https://doi.org/10.25077/jmua.14.1.14-30.2025.

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This study aims to examine the mathematical model of meningitis transmission as a deterministic model. The model includes five compartments: susceptible (S), carrier (C), infected (I), treatment (T), and recovered (R). We also consider vaccination and screening as interventions in disease transmission. In this work, we obtained two equilibrium points: disease-free equilibrium point and endemic equilibrium point. The next generation matrix is employed to compute the basic reproduction numbers ($R_0$). We also analyzed the sensitivity of parameters concerning $R_0$. If $R_0 < 1$, then the dis

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Megananda, Erzalina Ayu Satya, Cicik Alfiniyah, and Miswanto Miswanto. "Analisis kestabilan dan kontrol optimal model matematika penyebaran penyakit Ebola dengan variabel kontrol berupa karantina." Jambura Journal of Biomathematics (JJBM) 2, no. 1 (2021): 29–41. http://dx.doi.org/10.34312/jjbm.v2i1.10258.

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Ebola disease is an infectious disease caused by a virus from the genus Ebolavirus and the family Filoviridae. Ebola disease is one of the most deadly diseases for human. The purpose of the thesis is to analyze the stability of the equilibrium point and to apply the optimal control of quarantine on a mathematical model of the spread of ebola. Model without control has two equilibria, non-endemic equilibrium and endemic equilibrium. The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is asymptotically stable if R0 1

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Nursamsi, Nursamsi. "Stability Analysis of Model tuberculosis Spread in Diabetes Mellitus Patients with Treatment Factors." Jurnal Matematika, Statistika dan Komputasi 17, no. 1 (2020): 50–60. http://dx.doi.org/10.20956/jmsk.v17i1.10245.

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Diabetes mellitus (Dm) is a disease associated with impaired immune function so it is more susceptible to get infections including Tuberculosis (Tb). Tb disease can also worsen blood sugar levels which can cause Dm disease. This study aims to analyze and determine the stability of the equilibrium point of the spread of Tb disease in patients with Dm with consideration nine compartments, which are susceptible Tb without Dm, susceptible Tb without Dm complication, susceptible Tb with Dm complication, expose Tb without Dm, expose Tb with Dm, infected Tb without Dm, infected Tb with Dm, recovered

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Yin, Zhe, Yongguang Yu, and Zhenzhen Lu. "Stability Analysis of an Age-Structured SEIRS Model with Time Delay." Mathematics 8, no. 3 (2020): 455. http://dx.doi.org/10.3390/math8030455.

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This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium po

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Diana, Arista Fitri, Muhammad Ibnu Hajar, Zakaria Bani Ikhtiyar, and Lathifatul Aulia. "Analisis Kestabilan Lokal Model Transmisi Demam Berdarah Dengue." Square : Journal of Mathematics and Mathematics Education 6, no. 1 (2024): 41–54. http://dx.doi.org/10.21580/square.2024.6.1.21018.

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Dengue fever transmission in Indonesia has an advanced amount. In this article, dynamic model of interaction between human and Aedes aegypti mosquitos is learned. The SEIRRD (Susceptible, Exposed, Infected, Recovered, Deceased) model is used in this article. The prurpose in this model is to describe the stability of dengue transmission, so that we can analyze the developed of epidemic model in mathemtic field. Using NGM method to analyze basic reproduction number and applying Routh-Hurwitz criteria method to show the local stability of model. Then, two equilibrium points, called endemic and no

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Elkhadir, Saif H., Ali E. M. Saeed, and Abdelfatah Abasher. "Mathematical Model of Hepatitis B Virus With Effect of Vaccination and Treatments." International Journal of Analysis and Applications 20 (October 14, 2022): 53. http://dx.doi.org/10.28924/2291-8639-20-2022-53.

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In this paper, a mathematical model of hepatitis B virus with vaccination and treatments is studied, Stability analysis discussed and the disease-free equilibrium and endemic equilibrium points obtained, the basic reproductive number R0 determined and became the threshold for equilibrium points stability. The study showed when R0 < 1 the disease-free equilibrium point was stable, whereas R0 > 1 the virus is endemic and the endemic equilibrium point is stable. The sensitivity analysis for the parameters that could reduce the spread of hepatitis B virus is studied. Finally the numerical si

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Permatasari, Anindita Henindya, and Robertus Heri Soelistyo Utomo. "ANALYSIS OF TUBERCULOSIS DYNAMICAL MODEL WITH DIFFERENT EFFECTS OF TREATMENT." Journal of Fundamental Mathematics and Applications (JFMA) 4, no. 2 (2021): 193–202. http://dx.doi.org/10.14710/jfma.v4i2.12049.

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A tuberculosis model that integrates pre-infection and active infection stages along with two treatment parameters was studied. The model also considered the death rate due to pre-tuberculosis infection. The basic reproduction ratio was used to investigate the local and global stability of the equilibrium point. The local stability of uninfected equilibrium was analysed using Routh Hurwitz criteria. The existence of endemic equilibrium was given. After we achieved the endemic equilibrium, the global stability of the endemic equilibrium was analyzed using the Lyapunov function. A numerical simu

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De la Sen, Manuel, Santiago Alonso-Quesada, and Asier Ibeas. "On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility." Mathematics 9, no. 5 (2021): 520. http://dx.doi.org/10.3390/math9050520.

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A new discrete Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is proposed, and its properties of non-negativity and (both local and global) asymptotic stability of the solution sequence vector on the first orthant of the state-space are discussed. The calculation of the disease-free and the endemic equilibrium points is also performed. The model has the following main characteristics: (a) the exposed subpopulation is infective, as it is the infectious one, but their respective transmission rates may be distinct; (b) a feedback vaccination control law on the Susceptible is incor

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Jiayi, Li, Li Sixian, Shi Weixuan, Hu Manfeng, and Zhang Jingxiang. "Optimal Control and Stability Analysis of an SEIR Model with Infectious Force in Latent Period." Computational Intelligence and Neuroscience 2022 (June 15, 2022): 1–9. http://dx.doi.org/10.1155/2022/7596421.

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In this paper, an SEWIR epidemic model with the government control rate and infectious force in latent period is proposed. The conditions to the existence and uniqueness of disease-free and endemic equilibrium points in the SEWIR model are obtained. By using the Hurwitz criterion, the locally asymptotic stability of disease-free and endemic equilibrium points is proved. We show the global asymptotic stability of the disease-free equilibrium point by the construction of Lyapunov function and LaSalle invariance principle. The globally asymptotic stability of the endemic equilibrium is verified b

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Kaveri Kanchan Kumari. "Stability of Malicious Object in SIEQAR Model." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 2023–28. https://doi.org/10.52783/cana.v32.4443.

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The proposed model is SIEQAR ( Susceptible-Infected-Exposed-Quarantine-Antidotal-Recovered) which is extension of SAIR model. In this model we discussed Basic Reproduction number for MFE ( Malware Free Equilibrium) point. We discussed about Local stability at that point, also Endemic equilibrium point ids discussed.

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Perdana Putra, Septiangga Van Nyek, Agus Suryanto, and Nur Shofianah. "Dynamical Analysis of a Fractional Order HIV/AIDS Model." JTAM (Jurnal Teori dan Aplikasi Matematika) 5, no. 1 (2021): 14. http://dx.doi.org/10.31764/jtam.v5i1.3224.

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This article discusses a dynamical analysis of the fractional-order model of HIV/AIDS. Biologically, the rate of subpopulation growth also depends on all previous conditions/memory effects. The dependency of the growth of subpopulations on the past conditions is considered by applying fractional derivatives. The model is assumed to consist of susceptible, HIV infected, HIV infected with treatment, resistance, and AIDS. The fractional-order model of HIV/AIDS with Caputo fractional-order derivative operators is constructed and then, the dynamical analysis is performed to determine the equilibriu

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Musafir, Raqqasyi Rahmatullah, Agus Suryanto, and Isnani Darti. "Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination." Communication in Biomathematical Sciences 4, no. 2 (2021): 106–24. http://dx.doi.org/10.5614/cbms.2021.4.2.3.

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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 investigat

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Harianto, Joko, and Inda Puspita Sari. "ANALISIS KESTABILAN LOKAL TITIK EKUILIBRIUM MODEL EPIDEMI SEIV DENGAN PERTUMBUHAN LOGISTIK." Majalah Ilmiah Matematika dan Statistika 22, no. 1 (2022): 59. http://dx.doi.org/10.19184/mims.v22i1.30174.

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The SEIV model uses population growth which is assumed to follow logistical growth. The model is studied then analyzed. The analysis shows that the non-endemic (disease-free) equilibrium point is locally asymptotically stable when the basic reproduction number less than one, while the endemic equilibrium point is locally asymptotically stable when the basic reproduction number greater than one. Then a numerical simulation was carried out using Maple software to support the results of the local stability analysis of the equilibrium point. Based on numerical simulations, it shows that a disease

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Khofifah Ichawati and Budi Priyo Prawoto. "Dynamics of SARS-CoV-2 Spread Model with Vaccine Administration and Use of Masks." Jurnal Matematika MANTIK 8, no. 1 (2022): 18–27. http://dx.doi.org/10.15642/mantik.2022.8.1.18-27.

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The purpose of this study was to construct and determine the dynamics of the mathematical model of the reach of SARS-CoV-2 with the provision of vaccines and the use of masks. In this study, the modified SEIR model was used with the stages of conducting a literature study on mathematical modeling of the SARS-CoV-2 virus, compiling initial assumptions, making compartment diagrams, constructing mathematical models, determining equilibrium points, determining basic reproduction numbers, conducting stability analysis and synchronization of analysis results by performing numerical simulations. In t

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