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Journal articles on the topic 'Disease-free equilibrium'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Xu, Jinhu, Wenxiong Xu, and Yicang Zhou. "Analysis of a delayed epidemic model with non-monotonic incidence rate and vertical transmission." International Journal of Biomathematics 07, no. 04 (2014): 1450041. http://dx.doi.org/10.1142/s1793524514500417.

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A delayed SEIR epidemic model with vertical transmission and non-monotonic incidence is formulated. The equilibria and the threshold of the model have been determined on the bases of the basic reproduction number. The local stability of disease-free equilibrium and endemic equilibrium is established by analyzing the corresponding characteristic equations. By comparison arguments, it is proved that, if R0 < 1, the disease-free equilibrium is globally asymptotically stable. Whereas, the disease-free equilibrium is unstable if R0 > 1. Moreover, we show that the disease is permanent if the b

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2

Moghadas, S. M., and A. B. Gumel. "An epidemic model for the transmission dynamics of HIV and another pathogen." ANZIAM Journal 45, no. 2 (2003): 181–93. http://dx.doi.org/10.1017/s1446181100013250.

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AbstractA five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.

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3

Chukwu, C. W., and F. Nyabadza. "A Theoretical Model of Listeriosis Driven by Cross Contamination of Ready-to-Eat Food Products." International Journal of Mathematics and Mathematical Sciences 2020 (March 9, 2020): 1–14. http://dx.doi.org/10.1155/2020/9207403.

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Cross contamination that results in food-borne disease outbreaks remains a major problem in processed foods globally. In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. A contamination threshold ℛwf is determined. Analysis of the model shows that the disease-free equilibrium point is locally stable for ℛwf<1

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4

Lu, Jinna, Xiaoguang Zhang, and Rui Xu. "Global stability and Hopf bifurcation of an eco-epidemiological model with time delay." International Journal of Biomathematics 12, no. 06 (2019): 1950062. http://dx.doi.org/10.1142/s1793524519500621.

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In this paper, an eco-epidemiological model with time delay representing the gestation period of the predator is investigated. In the model, it is assumed that the predator population suffers a transmissible disease and the infected predators may recover from the disease and become susceptible again. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free and coexistence equilibria are established, respectively. By means of Lyapunov functionals and LaSalle’s invariance principle, sufficie

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5

Ah, Nurul Imamah, Wuryansari Muharini Kusumawinahyu, Agus Suryanto, and Trisilowati Trisilowati. "The Dynamics of a Predator-Prey Model Involving Disease Spread In Prey and Predator Cannibalism." Jambura Journal of Biomathematics (JJBM) 4, no. 2 (2023): 119–25. http://dx.doi.org/10.37905/jjbm.v4i2.21495.

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In this article, dynamics of predator prey model with infection spread in prey and cannibalism in predator is analyzed. The model has three populations, namely susceptible prey, infected prey, and predator. It is assumed that there is no migration in both prey and predator populations. The dynamical analysis shows that the model has six equilibria, namely the trivial equilibrium point, the prey extinction point, the disease free and predator extinction equilibrium point, the disease-free equilibrium point, the predator extinction equilibrium point, and the coexistence equilibrium point. The fi

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6

Lotfi, El Mehdi, Mehdi Maziane, Khalid Hattaf, and Noura Yousfi. "Partial Differential Equations of an Epidemic Model with Spatial Diffusion." International Journal of Partial Differential Equations 2014 (February 10, 2014): 1–6. http://dx.doi.org/10.1155/2014/186437.

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The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate. The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. By means of Lyapunov functional, the global stability of both equilibria is investigated. More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the ba

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7

A. Sabarmathi, C. Pooja ,. "A Fractional Order Approach in the Eco-epidemiological Model of Sugarcane Grassy Shoot Disease Using Controls." Tuijin Jishu/Journal of Propulsion Technology 44, no. 4 (2023): 5909–15. http://dx.doi.org/10.52783/tjjpt.v44.i4.2024.

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In this paper, an eco-epidemiological model for grassy shoot disease with controls is formed and analyzed using Fractional Differential Equations. The infection-free and endemic equilibriums of the model are obtained. Using the Next generation matrix approach, the basic reproduction number is calculated. The local stability of infection-free equilibrium for integer and fractional order is analyzed. The global stability of the equilibria is found using the Lyapunov function. The sensitive parameters which spread the grassy shoot disease are identified using sensitivity analysis.

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8

Mangongo Tinda, Yves, Jean-Pierre Lueteta Mulenda, and Josaphat Di-Phanzu Ndelo. "ANALYSIS OF THE DYNAMICS OF HELICOBACTER PYLORI IN THE PRESENCE OF CONCENTRATION OF CO2 AND IMMUNE SYSTEM." Journal Africain des Sciences 1, no. 1 (2024): 46–50. http://dx.doi.org/10.70237/jafrisci.2024.v1.i1.05.

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In this paper, we present a mathematical model describing the dynamics of Helicobacter pylori population in the presence of 〖CO〗_2 and the immune system. We analyze the mathematical and biological meaningful of the model. We analyze the equilibrium of the model. This analysis shows the presence of two types of equilibrium. The first one occurs in the absence of the immune response and when there is no 〖CO〗_2 in the stomach, called “disease-free equilibrium”. The second equilibriums, called “endemic equilibriums”, occur in the presence of immune response and when the concentration of 〖CO〗_2 is

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9

LIU, YIPING, and JING-AN CUI. "THE IMPACT OF MEDIA COVERAGE ON THE DYNAMICS OF INFECTIOUS DISEASE." International Journal of Biomathematics 01, no. 01 (2008): 65–74. http://dx.doi.org/10.1142/s1793524508000023.

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In this paper, we give a compartment model to discuss the influence of media coverage to the spreading and controlling of infectious disease in a given region. The model exhibits two equilibria: a disease-free and a unique endemic equilibrium. Stability analysis of the models shows that the disease-free equilibrium is globally asymptotically stable if the reproduction number (ℝ0), which depends on parameters, is less than unity. But if ℝ0 > 1, it is shown that a unique endemic equilibrium appears, which is asymptotically stable. On a special case, the endemic equilibrium is globally stable.

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10

Khan, Muhammad Altaf, Yasir Khan, Sehra Khan, and Saeed Islam. "Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate." International Journal of Biomathematics 09, no. 05 (2016): 1650068. http://dx.doi.org/10.1142/s1793524516500686.

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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 i

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11

Olopade, Isaac A., I. T. Mohammed, M. E. Philemon, et al. "A Study of a Class Continuous SIR Epidemic Model with History." Journal of Basics and Applied Sciences Research 2, no. 1 (2024): 54–60. http://dx.doi.org/10.33003/jobasr-2024-v2i1-28.

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The SIR model, an epidemiological model, divides a population into three compartments: Susceptible (S), Infected (I), and Recovered (R). It is widely used to understand the spread of infectious diseases and predict epidemic outcomes based on factors such as transmission rates and population dynamics. A deterministic epidemic mathematical model to describe the transmission dynamics of an infectious disease was constructed and analyzed by incorporating memory term which provides information on the current and past disease states. The model revealed two key equilibria: a disease-free equilibrium

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12

Zhonghua, Zhang, and Suo Yaohong. "Stability and Sensitivity Analysis of a Plant Disease Model with Continuous Cultural Control Strategy." Journal of Applied Mathematics 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/207959.

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In this paper, a plant disease model with continuous cultural control strategy and time delay is formulated. Then, how the time delay affects the overall disease progression and, mathematically, how the delay affects the dynamics of the model are investigated. By analyzing the transendental characteristic equation, stability conditions related to the time delay are derived for the disease-free equilibrium. Specially, whenR0=1, the Jacobi matrix of the model at the disease-free equilibrium always has a simple zero eigenvalue for allτ≥0. The center manifold reduction and the normal form theory a

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13

Khabouze, Mostafa, Khalid Hattaf, and Noura Yousfi. "Stability Analysis of an Improved HBV Model with CTL Immune Response." International Scholarly Research Notices 2014 (October 29, 2014): 1–8. http://dx.doi.org/10.1155/2014/407272.

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To better understand the dynamics of the hepatitis B virus (HBV) infection, we introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms. The local stability of the disease-free equilibrium and the chronic infection equilibrium is obtained via characteristic equations. Furthermore, the global stability of both equilibria is established by using two techniques, the direct Lyapunov method for the disease

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14

Prawoto, Budi Priyo, Dimas Avian Maulana, and Yuliani Puji Astuti. "The behaviour of measles transmission in three different populations." MATEC Web of Conferences 197 (2018): 01004. http://dx.doi.org/10.1051/matecconf/201819701004.

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SIR Model can be employed to model the transmission of either fatal or non-fatal disease within a closed population based on certain assumptions. In this paper, the behaviour of non-fatal diseases transmission model is observed from three types of population, that is (i) increasing population, (ii) constant population, (iii) decreasing population. This paper acquired two equilibria, i.e, the disease-free equilibrium point [see formula in PDF] and the endemic equilibrium point [see formula in PDF]. At the disease-free equilibrium, the behaviour of the model is stable when [see formula in PDF],

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15

Hidayat, Dayat, and Edwin Setiawan Nugraha. "Epidemic Model Analysis of Covid-19." E3S Web of Conferences 328 (2021): 06002. http://dx.doi.org/10.1051/e3sconf/202132806002.

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Covid-19 is a very extraordinary case not only in one country but all countries in the world. The number of deaths caused by Covid-19 is very large and the rate of spread of this disease is very high and fast. In this paper, we perform an analysis of a covid-19 epidemic model. This model is a development of the SEIR model in general which is equipped with a Quarantine (Q), Fatality (F) compartment, and there is a separation between detected and undetected infected people (I). Our analysis shows that there are two equilibria, namely, disease free equilibrium and endemic equilibrium. by using, L

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16

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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17

Gebremeskel, Abadi Abay, Hailay Weldegiorgis Berhe, and Adugna Temesgen Abay. "A Mathematical Modelling and Analysis of COVID-19 Transmission Dynamics with Optimal Control Strategy." Computational and Mathematical Methods in Medicine 2022 (November 9, 2022): 1–15. http://dx.doi.org/10.1155/2022/8636530.

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We proposed a deterministic compartmental model for the transmission dynamics of COVID-19 disease. We performed qualitative and quantitative analysis of the deterministic model concerning the local and global stability of the disease-free and endemic equilibrium points. We found that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity, while the endemic equilibrium point becomes locally asymptotically stable if the basic reproduction number is above unity. Furthermore, we derived the global stability of both the disease-free and e

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18

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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19

Yan, Caijuan, and Jianwen Jia. "Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/109372.

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We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratioℛ0<1, we discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov functional. Ifℛ0>1, we obtain sufficient conditions under which the

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20

Anteneh, Alemzewde Ayalew, Yezbalem Molla Bazezew, and Shanmugasundaram Palanisamy. "Mathematical Model and Analysis on the Impact of Awareness Campaign and Asymptomatic Human Immigrants in the Transmission of COVID-19." BioMed Research International 2022 (May 28, 2022): 1–13. http://dx.doi.org/10.1155/2022/6260262.

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In this study, an autonomous type deterministic nonlinear mathematical model that explains the transmission dynamics of COVID-19 is proposed and analyzed by considering awareness campaign between humans and infectives of COVID-19 asymptomatic human immigrants. Unlike some of other previous model studies about this disease, we have taken into account the impact of awareness c between humans and infectives of COVID-19 asymptomatic human immigrants on COVID-19 transmission. The existence and uniqueness of model solutions are proved using the fundamental existence and uniqueness theorem. We also s

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21

Samanta, Sudip. "Study of an epidemic model with Z-type control." International Journal of Biomathematics 11, no. 07 (2018): 1850084. http://dx.doi.org/10.1142/s1793524518500845.

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In the present paper, an epidemic model with Z-type control mechanism has been proposed and analyzed to explore the disease control strategy on an infectious disease outbreak. The uncontrolled model can have a disease-free equilibrium and an endemic equilibrium. The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived. It is also observed that the disease-free equilibrium is globally asymptotically stable if [Formula: see text], whereas the endemic equilibrium is globally asymptotically stable if [Formula: see text]. The model is furthe

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22

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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23

Adeyemo, K. M. "Local Stability Analysis of Onchocerciasis Transmission Dynamics With Nonlinear Incidence Functions in Two Interacting Populations." European Journal of Mathematical Analysis 3 (August 7, 2023): 22. http://dx.doi.org/10.28924/ada/ma.3.22.

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A deterministic compartmental model for the transmission dynamics of onchocerciasis with nonlinear incidence functions in two interacting populations is studied. The model is qualitatively analyzed to investigate its local asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using Routh-Hurwitz criteria, that the disease-free equilibrium is locally asymptotically stable when the associated basic reproduction number is less than the unity. When the basic reproduction number is greater than the unity, we prove the existence of a locally asymptotically stable ende

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24

Almuqati, B. M., and F. M. Allehiany. "Global stability of a multi-group delayed epidemic model with logistic growth." AIMS Mathematics 8, no. 10 (2023): 23046–61. http://dx.doi.org/10.3934/math.20231173.

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<abstract><p>In this work, we aim to investigate the mechanism of a multi-group epidemic model taking into account the influences of logistic growth and delay time distribution. Despite the importance of the logistic growth effect in such models, its consideration remains rare. We show that $ \mathcal{R}_0 $ has a crusher role in the global stability of a disease-free and endemic equilibria. That is, if $ \mathcal{R}_0 $ is less than or equal to one, then the disease-free equilibrium is globally asymptotically stable, whereas, if $ \mathcal{R}_0 $ is greater than one, then a unique

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25

Aligaz, Achamyelesh A., and Justin M. W. Munganga. "MODELLING THE TRANSMISSION DYNAMICS OF CONTAGIOUS BOVINE PLEUROPNEUMONIA IN THE PRESENCE OF ANTIBIOTIC TREATMENT WITH LIMITED MEDICAL SUPPLY." Mathematical Modelling and Analysis 26, no. 1 (2021): 1–20. http://dx.doi.org/10.3846/mma.2021.11795.

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We present and analyze a mathematical model of the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) in the presence of antibiotic treatment with limited medical supply. We use a saturated treatment function to model the effect of delayed treatment. We prove that there exist one disease free equilibrium and at most two endemic equilibrium solutions. A backward bifurcation occurs for small values of delay constant such that two endemic equilibriums exist if Rt (R*t,1); where, Rt is the treatment reproduction number and R*t is a threshold such that the disease dies out if and per

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26

Pambudi, Adiluhung Setya, Fatmawati Fatmawati, and Windarto Windarto. "Analisis Kontrol Optimal Model Matematikan Penyebaran Penyakit Mosaic pada Tanaman Jarak Pagar." Contemporary Mathematics and Applications (ConMathA) 1, no. 2 (2020): 104. http://dx.doi.org/10.20473/conmatha.v1i2.17386.

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Mosaic disease is an infectious disease that attacks Jatropha curcas caused by Begomoviruses. Mosaic disease can be transmitted through the bite of a whitefly as a vector. In this paper, we studied a mathematical model of mosaic disease spreading of Jatropha curcas with awareness effect. We also studied the effect of prevention and extermination strategies as optimal control variables. Based on the results of the model analysis, we found two equilibriums namely the mosaic-free equilibrium and the endemic equilibrium. The stability of equilibriums and the existence of endemic equilibrium depend

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Rattanakul, Chontita, and Inthira Chaiya. "A mathematical model for predicting and controlling COVID-19 transmission with impulsive vaccination." AIMS Mathematics 9, no. 3 (2024): 6281–304. http://dx.doi.org/10.3934/math.2024306.

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<abstract><p>This study examines an epidemiological model known as the susceptible-exposed-infected-hospitalized-recovered (SEIHR) model, with and without impulsive vaccination strategies. First, the model was analyzed without impulsive vaccination in the presence of a reinfection effect. Subsequently, it was studied as part of a periodic impulsive vaccination strategy targeting the susceptible population. These vaccination impulses were administered in very brief intervals at specific time instants, with a fixed time gap between each impulse. The two approaches can be modified to

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Gómez, Miller Cerón, Eduardo Ibarguen Mondragon, and Paulo Cesar Carmona Tabares. "Mathematical model of evasion of immune system by virus." Journal of Interdisciplinary Mathematics 26, no. 4 (2023): 733–45. http://dx.doi.org/10.47974/jim-1508.

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Virus needs to infect cells to spread the disease in the host and to achieve this, they have developed specific tactics to evade the immune system, which is in charge of trying to prevent any infection. In this way, we develop a mathematical model to represent the evasion of immune system by virus using a non-monotonic functional response describing an antipredator behavior, where the virus is the prey and the immune cells are the predator. We found four equilibrium points, the disease free equilibrium, immune evasion equilibrium and two immune activation equilibrium points. The disease free e

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Agusto, F. B., J. Cook, P. D. Shelton, and M. G. Wickers. "Mathematical Model of MDR-TB and XDR-TB with Isolation and Lost to Follow-Up." Abstract and Applied Analysis 2015 (2015): 1–21. http://dx.doi.org/10.1155/2015/828461.

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We present a deterministic model with isolation and lost to follow-up for the transmission dynamics of three strains ofMycobacterium tuberculosis(TB), namely, the drug sensitive, multi-drug-resistant (MDR), and extensively-drug-resistant (XDR) TB strains. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the model has locally asymptotically stable (LAS) disease-free equilibrium when the associated reproduction number is less than unity. Furthermore, the model undergoes in the pre

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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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Ge, Shao Ting, Gong You Tang, Xue Yang, Qi Lei Xu, Hao Yu, and Pei Dong Wang. "Stability Analysis of Computer Virus Model System in Networks." Applied Mechanics and Materials 278-280 (January 2013): 2033–38. http://dx.doi.org/10.4028/www.scientific.net/amm.278-280.2033.

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This paper considers stability analysis of a discrete-time computer virus model in networks. The disease-free equilibrium and the disease equilibrium are first derived from the mathematical model. Then the sufficient condition of stability for the disease-free equilibrium is obtained by the first Lyapunov method. And the sufficient conditions of stability for the disease equilibrium are given by disc theorem. Simulation results demonstrate the effectiveness of the stability conditions.

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32

Sugiarto, Sigit, Ratnah Kurniati MA, and Sugian Nurwijaya. "DYNAMICAL SYSTEM FOR COVID-19 OUTBREAK WITHIN VACCINATION TREATMENT." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 2 (2023): 0919–30. http://dx.doi.org/10.30598/barekengvol17iss2pp0919-0930.

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Covid-19 is a deadly infectious disease that occurs throughout the world. Therefore, it is necessary to prevent the transmission of Covid-19 such as vaccination. The purpose of this research is to modify the model of the spread of the Covid-19 disease from the previous model. The equilibrium points and the basic reproduction number ( ) of the modified model is determined. Then a stability analysis was carried out and a numerical simulation was carried out to see the dynamics of the population that occurred. The analysis performed on the model obtained two equilibriums, namely the disease-freee

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Ozair, Muhammad, Abid Ali Lashari, Il Hyo Jung, Young Il Seo, and Byul Nim Kim. "Stability Analysis of a Vector-Borne Disease with Variable Human Population." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/293293.

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A mathematical model of a vector-borne disease involving variable human population is analyzed. The varying population size includes a term for disease-related deaths. Equilibria and stability are determined for the system of ordinary differential equations. IfR0≤1, the disease-“free” equilibrium is globally asymptotically stable and the disease always dies out. IfR0>1, a unique “endemic” equilibrium is globally asymptotically stable in the interior of feasible region and the disease persists at the “endemic” level. Our theoretical results are sustained by numerical simulations.

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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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35

Wang, Zizi, and Zhiming Guo. "Dynamical Behavior of a New Epidemiological Model." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/854528.

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A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain timeτ. The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive numberR0is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided thatR0≤1; ifR0>1, then there exist

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36

Buyukadalı, Cemil. "STABILITY ANALYSIS OF A CAPUTO TYPE FRACTIONAL WATERBORNE INFECTIOUS DISEASE MODEL." Journal of Mathematical Analysis 13, no. 5 (2022): 1–11. https://doi.org/10.54379/jma-2022-5-1.

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We introduce a Caputo type fractional waterborne infectious dis- ease model. Disease transmissions of this model has saturation effect of infec- tious individuals on both human-to-human and environment-to-human con- tacts. For this model we find sufficient conditions for local stability of disease free and endemic epidemic equilibriums by linearization and global stability of disease free equilibrium by Liapunov method. Appropriate numerical simula- tions are also given to verify the results.

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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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Naim, Mouhcine, and Fouad Lahmidi. "Analysis of a Deterministic and a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis and Specific Functional Response." Discrete Dynamics in Nature and Society 2020 (May 26, 2020): 1–11. http://dx.doi.org/10.1155/2020/5362716.

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The purpose of this paper is to investigate the stability of a deterministic and stochastic SIS epidemic model with double epidemic hypothesis and specific nonlinear incidence rate. We prove the local asymptotic stability of the equilibria of the deterministic model. Moreover, by constructing a suitable Lyapunov function, we obtain a sufficient condition for the global stability of the disease-free equilibrium. For the stochastic model, we establish global existence and positivity of the solution. Thereafter, stochastic stability of the disease-free equilibrium in almost sure exponential and p

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Adeyemo, K. M. "Global Stability Analysis of Onchocerciasis Transmission Dynamics with Vigilant Compartment in Two Interacting Populations." European Journal of Mathematical Analysis 4 (April 15, 2024): 9. http://dx.doi.org/10.28924/ada/ma.4.9.

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A deterministic compartmental model for the transmission dynamics of onchocerciasis with vigilant compartment in two interacting populations is studied. The model is qualitatively analyzed to investigate its global asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using a linear Lyapunov function, that the disease-free equilibrium is globally asymptotically stable when the associated basic reproduction number, R0<1. When the basic reproduction number R0>1, under some certain conditions on the model parameters, we prove that the endemic equilibrium is g

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Sun, Bei, Xue Zhang, and Marco Tosato. "Effects of Coinfection on the Dynamics of Two Pathogens in a Tick-Host Infection Model." Complexity 2020 (May 28, 2020): 1–14. http://dx.doi.org/10.1155/2020/5615173.

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As both ticks and hosts may carry one or more pathogens, the phenomenon of coinfection of multiple tick-borne diseases becomes highly relevant and plays a key role in tick-borne disease transmission. In this paper, we propose a coinfection model involving two tick-borne diseases in a tick-host population and calculate the basic reproduction numbers at the disease-free equilibrium and two boundary equilibria. To explore the impact of coinfection, we also derive the invasion reproduction numbers which indicate the potential of a pathogen to persist when another pathogen already exists in tick an

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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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Khan, Muhammad Altaf, Yasir Khan, Taj Wali Khan, and Saeed Islam. "Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology." International Journal of Biomathematics 10, no. 07 (2017): 1750096. http://dx.doi.org/10.1142/s1793524517500966.

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In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For [Formula: see text], the disease-free equilibrium is stable both locally and globally and for [Formula: see text], the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are prese

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LIU, LILI, XINZHI REN, and XIANNING LIU. "DYNAMICAL BEHAVIORS OF AN INFLUENZA EPIDEMIC MODEL WITH VIRUS MUTATION." Journal of Biological Systems 26, no. 03 (2018): 455–72. http://dx.doi.org/10.1142/s0218339018500201.

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Influenza virus mutates frequently. This poses immense challenges to prevent the spread of influenza. This paper aims to investigate an influenza epidemic model in which influenza virus can mutate into a mutant influenza virus. We find a threshold condition that determines the stability of the disease-free equilibrium. Two equilibria may also exist: mutant-dominant equilibrium and endemic equilibrium. We show that the mutant-dominant equilibrium is globally asymptotically stable under some biological feasible conditions. Furthermore, the influenza is endemic in the sense of permanence if and o

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Wang, Jinghai. "Analysis of an SEIS Epidemic Model with a Changing Delitescence." Abstract and Applied Analysis 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/318150.

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An SEIS epidemic model with a changing delitescence is studied. The disease-free equilibrium and the endemic equilibrium of the model are studied as well. It is shown that the disease-free equilibrium is globally stable under suitable conditions. Moreover, we also show that the unique endemic equilibrium of the system is globally asymptotically stable under certain conditions.

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Wang, Xiaoyan, Junyuan Yang, and Fengqin Zhang. "Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age." Journal of Applied Mathematics 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/429567.

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A coepidemic arises when the spread of one infectious disease stimulates the spread of another infectious disease. Recently, this has happened with human immunodeficiency virus (HIV) and tuberculosis (TB). The density of individuals infected with latent tuberculosis is structured by age since latency. The host population is divided into five subclasses of susceptibles, latent TB, active TB (without HIV), HIV infectives (without TB), and coinfection class (infected by both TB and HIV). The model exhibits three boundary equilibria, namely, disease free equilibrium, TB dominated equilibrium, and

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Hove-Musekwa, S. D., and F. Nyabadza. "The Dynamics of an HIV/AIDS Model with Screened Disease Carriers." Computational and Mathematical Methods in Medicine 10, no. 4 (2009): 287–305. http://dx.doi.org/10.1080/17486700802653917.

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The presence of carriers usually complicates the dynamics and prevention of a disease. They are not recognized as disease cases themselves unless they are screened and they usually spread the infection without them being aware. We argue that this has been one of the major causes of the spread of human immunodeficiency virus (HIV). We propose, in this paper, a model for the heterogeneous transmission of HIV/acquired immunodeficiency syndrome in the presence of disease carriers. The model allows us to assess the role of screening, as an intervention program that can slow the epidemic. A threshol

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Khan, Muhammad Altaf, Yasir Khan, Qaiser Badshah, and Saeed Islam. "Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination." International Journal of Biomathematics 08, no. 06 (2015): 1550082. http://dx.doi.org/10.1142/s1793524515500825.

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In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number [Formula: see text]. If the basic reproduction number [Formula: see text], the disease-free equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number [Formula: see text], the dis

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Widayati, Ratna. "Global Stability of Covid-19 Disease Free Based on Sivrs Model." Jurnal Matematika, Statistika dan Komputasi 19, no. 2 (2023): 400–411. http://dx.doi.org/10.20956/j.v19i2.24386.

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This study discusses the spread of the Covid-19 disease by including new variant variables. The model used by SIVRS assumes there are deaths caused by Covid-19 and the new variant Covid-19. In addition, individuals who have been infected with the new variant of Covid-19 can recover. Based on the model, disease-free equilibrium points and endemic equilibrium points are obtained. The analysis was carried out around the disease-free equilibrium point and the result was that the global asymptotically stable disease-free equilibrium point with the condition R0<1. Furthermore, a simulation was ca

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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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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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