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Journal articles on the topic 'Disease free equilibrium point (DFEP)'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Ud din, Rahim, and Muhammad Shoaib Ari. "Numerical Analysis of Deterministic and Stochastic Model of COVID-19 Co-infection with Influenza." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 6005. https://doi.org/10.29020/nybg.ejpam.v18i2.6005.

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The dynamics of co-infection model of SARS-Cov-2 and influenza is presented in this paper. A detailed analysis is conducted on the possible effects of the influenza vaccination alone as well as the combined effect of both vaccinations on the co-infection dynamics. The two diseases' basic reproduction numbers utilizing the next-generation matrix method.Endemic equilibrium point (EEP), and disease free equilibrium points (DFEP) are calculated for deterministic model. The global stability of the model equilibrium is demonstrated using the Lyapunov function function, and the local stability is dis

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Oluwafemi, T. J., N. I. Akinwande, R. O. Olayiwola, A. F. Kuta, and E. Azuaba. "Co-infection Model Formulation to Evaluate the Transmission Dynamics of Malaria and Dengue Fever Virus." Journal of Applied Sciences and Environmental Management 24, no. 7 (2020): 1187–95. http://dx.doi.org/10.4314/jasem.v24i7.10.

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A mathematical model of the co-infection dynamics of malaria and dengue fever condition is formulated. In this work, the Basic reduction number is computed using the next generation method. The diseasefree equilibrium (DFE) point of the model is obtained. The local and global stability of the disease-free equilibrium point of the model is established. The result show that the DFE is locally asymptotically stable if the basic reproduction number is less than one but may not be globally asymptotically stable.  Keywords: Malaria; Dengue Fever; Co-infection; Basic reproduction number; Diseas

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3

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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Saputra, Handika Lintang, Isnani Darti, and Agus Suryanto. "Analysis of SVEIL Model of Tuberculosis Disease Spread with Imperfect Vaccination." JTAM (Jurnal Teori dan Aplikasi Matematika) 7, no. 1 (2023): 125. http://dx.doi.org/10.31764/jtam.v7i1.11033.

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This study proposes a SVEIL model of tuberculosis disease spread with imperfect vaccination. Susceptible individuals can receive imperfect vaccination, but over the time the vaccine efficacy will decrease. Vaccinated individuals are in vulnerable class since they still have probability to get reinfected. The proposed model includes treatment for both high-risk latent and active TB patients. In fact, after getting appropriate treatment (get recovered) the individuals still have bacteria in their body and it is classified to low-risk laten class. Dynamical behaviour of the model is analyzed to u

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Danhausa, A. A., E. E. Daniel, C. J. Shawulu, A. M. Nuhu, and L. Philemon. "Drug-sensitivity and passive immunity mathematical epidemiological model for tuberculosis." Journal of Applied Sciences and Environmental Management 25, no. 9 (2021): 1661–70. http://dx.doi.org/10.4314/jasem.v25i9.18.

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Regardless of many decades of research, the widespread availability of a vaccine and more recently highly visible WHO efforts to promote a unified global control strategy, Tuberculosis remains a leading cause of infectious mortality. In this paper, a Mathematical Model for Tuberculosis Epidemic with Passive Immunity and Drug-Sensitivity is presented. We carried out analytical studies of the model where the population comprises of eight compartments: passively immune infants, susceptible, latently infected with DS-TB. The Disease Free Equilibrium (DFE) and the Endemic Equilibrium (EE) points we

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Adiela, Chukwumela, and Iyai Davies. "Effect of Time Delay in the Stability Analysis of Cholera Epidemic-Endemic Disease Model." European Journal of Theoretical and Applied Sciences 2, no. 3 (2024): 281–97. https://doi.org/10.59324/ejtas.2024.2(3).24.

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Cholera as a disease is a kind of acute diarrhea caused by bacteria <em>Vibrio cholerae</em>. A nonlinear delayed mathematical model with environmental factor for the spread of infectious disease cholera is proposed and analyzed. A mathematical model for cholera was improved by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. It is assumed that all susceptible are affected by carrier population density. The model is analyzed by stability theory of differential eq

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Flaviana, Priscilla Persulessy, Siantu Paian, and Jaharuddin. "Mathematics Model Development Deployment of Dengue Fever Diseases by Involve Human and Vectors Exposed Components." International Journal of Engineering and Management Research 8, no. 4 (2018): 46–53. https://doi.org/10.31033/ijemr.8.4.5.

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Dengue virus is one of virus that cause deadly disease was dengue fever. This virus was transmitted through bite of Aedes aegypti female mosquitoes that gain virus infected by taking food from infected human blood, then mosquitoes transmited pathogen to susceptible humans. Suppressed the spread and growth of dengue fever was important to avoid and prevent the increase of dengue virus sufferer and casualties. This problem can be solved with studied important factors that affected the spread and equity of disease by sensitivity index. The purpose of this research were to modify mathematical mode

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8

Ezekiel, Imekela D., Samuel A. Iyase, and Timothy A. Anake. "Stability and Hopf Bifurcation Analysis of an Infectious Disease Delay Model." WSEAS TRANSACTIONS ON MATHEMATICS 24 (March 14, 2025): 126–43. https://doi.org/10.37394/23206.2025.24.14.

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This paper investigated the stability of the dynamical behavior of the susceptible (S), infectious (I) and recovered (R) (SIR) disease epidemic model with intracellular time delay that is unable to stabilize the unstable interior non-hyperbolic equilibrium. The study employed characteristics and bifurcation methods for investigating conditions of stability and instability of the SIR disease epidemic model using the dimensionless threshold reproduction value 𝑅0 for the disease-free equilibrium (DFE) point and the endemic equilibrium point. The study confirms that disease-free equilibrium (DFE)

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9

Iqbal, Iqbal, Iqbal M. Batiha, Mohammad S. Hijazi, Issam Bendib, Adel Ouannas, and Nidal Anakira. "Fractional-Order SEIR Model for COVID-19: Finite-Time Stability Analysis and Numerical Validation." International Journal of Neutrosophic Science 26, no. 1 (2025): 266–82. https://doi.org/10.54216/ijns.260123.

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This paper investigates a fractional-order SEIR model to study the dynamics of infectious diseases, specifically COVID-19, by incorporating memory effects through fractional derivatives. The model’s formulation enhances the understanding of epidemic dynamics by considering disease transmission, recovery, and mortality rates under fractional calculus. Stability analyses are conducted for the disease-free equilibrium (DFE) and the pandemic fixed point (PFP), identifying critical conditions for finite-time stability using Lyapunov functions and fractional derivatives. Numerical simulations valida

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El Alami laaroussi, Adil, Mohamed El Hia, Mostafa Rachik, and Rachid Ghazzali. "Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy." Computational and Mathematical Methods in Medicine 2019 (September 30, 2019): 1–12. http://dx.doi.org/10.1155/2019/1732815.

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Despite advanced discoveries in cancerology, conventional treatments by surgery, chemotherapy, or radiotherapy remain ineffective in some situations. Oncolytic virotherapy, i.e., the involvement of replicative viruses targeting specific tumor cells, opens new perspectives for better management of this disease. Certain viruses naturally have a preferential tropism for the tumor cells; others are genetically modifiable to present such properties, as the lytic cycle virus, which is a process that represents a vital role in oncolytic virotherapy. In the present paper, we present a mathematical mod

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Mohammed S. Abdo, Mohammed Amood AL Kamarany, Khaled Ahmed Suhail, and Ahmed Suliman Majam. "Vaccination-based Measles Outbreak Model with Fractional Dynamics." Abhath Journal of Basic and Applied Sciences 1, no. 2 (2022): 6–10. http://dx.doi.org/10.59846/abhathjournalofbasicandappliedsciences.v1i2.439.

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The objective of this study is to create and evaluate a novel measles model that takes into account the impact of vaccination in Yemen and makes use of fractional piecewise Caputo derivatives. The theoretical aspect provides the disease-free equilibrium (DFE) points, the basic reproduction number (R0), and the biologically viable region of the proposed model. We also deduce the results for uniqueness using the Banach fixed point theorem

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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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Verma, Vijai Shanker, Laxman Bahadur Kunwar, Archana Singh Bhadauria, and Vikash Rana. "AN SVIQR EPIDEMIC MODEL FOR COVID-19." South East Asian J. of Mathematics and Mathematical Sciences 18, no. 03 (2022): 101–22. http://dx.doi.org/10.56827/seajmms.2022.1803.9.

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We have proposed an SVIQR epidemic model for COVID-19 with vac- cination in this research. Some fundamental characteristics such as positivity of the solution, boundedness and invariance of the model are analyzed. Expressions for disease-free equilibrium (DFE) and endemic equilibrium (EE) points with certain criteria for existence are derived. Rigorous analysis of the model reveals that as- sociated DFE is locally asymptotically stable whenever the effective reproduction number is less than one. Also, the EE point is stable whenever certain restric- tions are satisfied. Sensitivity analysis is

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Vaz, Sandra, and Delfim F. M. Torres. "A Discrete-Time Compartmental Epidemiological Model for COVID-19 with a Case Study for Portugal." Axioms 10, no. 4 (2021): 314. http://dx.doi.org/10.3390/axioms10040314.

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Recently, a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) was presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) was analysed. Here, we propose an analogous discrete-time model and, using a suitable Lyapunov function, we prove the global stability of the DFE point. Using COVID-19 real data, we show, through numerical simulations, the consistence of the obtained theoretical results.

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15

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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16

Abd ElRaouf, Hazem M., Alhaytham M. Aref, Ahmed K. Elsherif, and Mohamed E. Khalifa. "Study and Analysis of Corona-Virus Transfer Dynamics using Enhanced SEIR Epidemic Model with Vaccination Effect." Journal of Physics: Conference Series 2304, no. 1 (2022): 012002. http://dx.doi.org/10.1088/1742-6596/2304/1/012002.

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Abstract Corona Virus Syndrome (COVID-19) is a contagious disease and it is considered one of the deadliest viruses ever known to humanity. In this work, the transmission dynamics of the COVID- 19 has been studied using an enhanced SEIR epidemic compartmental model with a vaccination compartment. This model divides the whole population into five categories: susceptible (S), exposed (E), infectious (I), recovered (R), and vaccinated (V). Firstly, Positivity, Existence and Uniqueness of solution are illustrated. Secondly, a mathematical analysis is done to study the equilibrium points of the mod

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17

O.A, Adedayo. "Mathematical Modeling of the Transmission Dynamics of Covid-19 with Quarantine and Hospitality Treatment." International Journal for Research in Applied Science and Engineering Technology 11, no. 5 (2023): 1893–905. http://dx.doi.org/10.22214/ijraset.2023.51834.

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Abstract: This study presents a COVID-19 epidemic disease model that has been tailored to fit the specific circumstances of world. The Nigerian population has been partitioned into seven subpopulations in this model system. These subpopulations include the Susceptible class, Exposed class, Symptomatic Infected class, Asymptomatically Infected class, Quarantined individuals, Hospitalised individuals, and Recovered individuals. The model was augmented with control measures parameters, specifically those related to hospitalisation and quarantine. The disease-free equilibrium and endemic equilibri

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18

Mangobi, James Uriel Livingstone. "SEIR MODEL SIMULATION WITH PART OF INFECTED MOSQUITO EGGS." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 3 (2023): 1641–52. http://dx.doi.org/10.30598/barekengvol17iss3pp1641-1652.

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Dengue hemorrhagic fever (DHF) is an acute febrile disease caused by the dengue virus, which is transmitted by various species of Aedes mosquitoes. The SEIR model is a mathematical model for studying the spread of dengue fever. In this model, it is assumed that some mosquito eggs have been infected because infected mosquitoes can transmit the virus to their eggs. The main vector of this disease is the Aedes albopictus mosquito. Analysis was carried out to assess the stability of the equilibrium point, and numerical simulations were carried out to see changes in population numbers due to change

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Kumar, Anuj, Yasuhiro Takeuchi, and Prashant K. Srivastava. "Stability switches, periodic oscillations and global stability in an infectious disease model with multiple time delays." Mathematical Biosciences and Engineering 20, no. 6 (2023): 11000–11032. http://dx.doi.org/10.3934/mbe.2023487.

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<abstract><p>A delay differential equation model of an infectious disease is considered and analyzed. In this model, the impact of information due to the presence of infection is considered explicitly. As information propagation is dependent on the prevalence of the disease, the delay in reporting the prevalence is an important factor. Further, the time lag in waning immunity related to protective measures (such as vaccination, self-protection, responsive behaviour etc.) is also accounted. Qualitative analysis of the equilibrium points of the model is executed and it is observed th

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20

Ayele, Tigabu Kasie, Emile Franc Doungmo Goufo, and Stella Mugisha. "Co-infection mathematical model for HIV/AIDS and tuberculosis with optimal control in Ethiopia." PLOS ONE 19, no. 12 (2024): e0312539. https://doi.org/10.1371/journal.pone.0312539.

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The co-epidemics of HIV/AIDS and Tuberculosis (TB) outbreak is one of a serious disease in Ethiopia that demands integrative approaches to combat its transmission. In contrast, epidemiological co-infection models often considered a single latent case and recovered individuals with TB. To bridge this gap, we presented a new optimal HIV-TB co-infection model that considers both high risk and low risk latent TB cases with taking into account preventive efforts of both HIV and TB diseases, case finding for TB and HIV/AIDS treatment. This study aimed to develop optimal HIV/AIDS-TB co-infection math

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21

Ghosh, Jayanta Kumar, Prahlad Majumdar, and Uttam Ghosh. "Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment." Mathematical Modelling of Natural Phenomena 16 (2021): 13. http://dx.doi.org/10.1051/mmnp/2021004.

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This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point (DFE) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, whi

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Jehangir, Hammad, Nigar Ali, Imtiaz Ahmad, Hazrat Younas, and Hijaz Ahmad. "Global Dynamics and Numerical Simulation of a Vaccinated Mathematical Model for Ebola Disease." Global Journal of Sciences 1, no. 1 (2024): 14–27. https://doi.org/10.48165/gjs.2024.1102.

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Rabies continues to be a major hazard to public health around the world, especially in developing countries. This article proposes an equation that describes the mechanics of animal-to-animal transmission of rabies, accounting for vaccination and infected immigrants as potential preventative strategies. The effective reproduction number (R0) was computed using the next-generation matrix (NGM) Method. The Routh–Hurwitz Criterion was utilized to identify the disease-free equilibrium point (DFE). It was shown to be unstable in all other cases and to exhibit local asymptotic stability if (R0 <

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Ouattara, Lassina, Harouna Ouedraogo, Dramane Ouedraogo, and Aboudramane Guiro. "Analysis and optimal control for SEIR mathematical modeling of COVID-19." Malaya Journal of Matematik 12, no. 04 (2024): 367–87. https://doi.org/10.26637/mjm1204/003.

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In this paper a mathematical model of SEIR type is formulated. represented by modeling the coronavirus epidemic. In this present study, we consider a mathematical model that incorporates the whole population and variability in transmission between reported and unreported populations. The global stability of the disease free equilibrium (DFE) point is established. The basic reproduction number R0 is calculated. We introduce into our model two controls which are vaccination ofsusceptible humans denoted by u and treatment of infected humans designed by v. In addition, this model takes into consid

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Aminu, M., M. O. Ibrahim, A. Mustafa, and I. Abdullahi. "STABILITY ANALYSIS OF A STAGED PROGRESSION HIV/AIDS MODEL WITH SCREENING AND CONDOM USAGE." Journal of Mathematical Sciences & Computational Mathematics 2, no. 2 (2021): 287–304. http://dx.doi.org/10.15864/jmscm.2208.

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In this Paper, a staged-progression model for HIV/AIDS transmission dynamics is formulated and analyzed to study the impact of Screening, Condom usage and Condom compliance. The local stability for the disease free equilibrium (DFE) was proved for Rc < 1 and Kransnoselki sublinearity trick was used to show that the endemic equilibrium (EE) is locally asymptotically stable for a special case whenever Rc > 1. Numerical simulation was also carried out to investigate the effects of screening unaware (unscreened) asymptomatic individuals and Condom compliance. The result shows the influence o

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SHARMA, SWARNALI, and G. P. SAMANTA. "ANALYSIS OF A CHLAMYDIA EPIDEMIC MODEL." Journal of Biological Systems 22, no. 04 (2014): 713–44. http://dx.doi.org/10.1142/s0218339014500296.

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In this paper, we have developed a five-compartmental epidemic model with Chlamydia infection. We have divided the total population into five classes, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase and recovered class. The basic reproduction number (R0) is calculated using the next-generation matrix method. The stability analysis of the model shows that the system is locally asymptotically stable at the disease-free equilibrium (DFE) E0when R0< 1. When R0> 1, an endemic equilibrium E1exists and the system becomes locally asymptotically stable

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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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S, K. Tiwari, Porwal P, and Mangal Neha. "Design and Investigation of Mathematical Model for the Vaccination and Transmission of Monkeypox Virus without Lifelong Immunity." Indian Journal of Science and Technology 16, no. 39 (2023): 3423–34. https://doi.org/10.17485/IJST/v16i39.1521.

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Abstract <strong>Objective:</strong> For the purpose of evaluating the potential for outbreaks of monkeypox (MPX) in a metropolitan region and defining necessary public health measures to restrict the spread of the virus through the use of a model of its dissemination, the preventive interventions have a critical role in the management of infectious diseases. The objective of this study is to assess the feasibility of managing and eliminating MPX through the use of voluntary vaccination and treatment measures. <strong>Methods:</strong> We developed two equilibriums for the model

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Edwiga, Renald. "Sensitivity Analysis and Numerical Simulation of a SEIV Basic Dog-Rabies Mathematical Model with Control." International Journal of Advances in Scientific Research and Engineering (ijasre) 5, no. 9 (2019): 142–48. https://doi.org/10.31695/IJASRE.2019.33526.

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<em>Rabies is a zoonotic, viral disease that causes acute inflammation of the brain in humans and other mammals. It is transmitted by the saliva of infected animals via bites, scratches or contact between open body parts of infectious dog and noninfectious. In this paper, we have analysed a SEIV (Susceptible-Exposed-Infectious-Vaccinated) mathematical model for dog-rabies whereby sensitivity analysis and numerical simulation of the model have been carried out, presented and discussed. According to the sensitivity indices of parameters used at DFE (Disease Free Equilibrium) point, an infection

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Saduri, Das . Tapan Sarkar . Prashant K. Srivastava . Pankaj Biswas. "Insights into TB-HIV Co-infection with Fast and Slow Progression and Reinfection in TB using NSFD Method." Journal of Innovation Sciences and Sustainable Technologies 4, no. 2 (2024): 113–43. https://doi.org/10.0525/JISST.2024512525.

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The global concern regarding the harmful impact of synergistic interactions between tuberculosis (TB) and human immunodeficiency virus (HIV) has become widespread. So, efforts to address these synergistic interactions are essential for improving public health outcomes and reducing the burden of both diseases. TB is highly contagious and individuals with HIV are more likely to develop active TB disease and become infectious. This leads to an increase in transmission of TB within communities, posing a public health threat. In this work, we explore a TB-HIV co-infection model that includes exogen

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Niu, Te. "Modeling dengue transmission in Singapore." Applied and Computational Engineering 2, no. 1 (2023): 984–91. http://dx.doi.org/10.54254/2755-2721/2/20220635.

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Dengue fever is a widespread epidemic that transmits between the vector mosquitoes and the host humans. It has long remained a threat to the public health for many countries since there is no effective treatment for it currently. Therefore, it is practically valuable to conduct research on the transmission of Dengue Fever virus to help combat Dengue Virus. Out of this purpose and to bridge the gap in the research of Dengue Fever, this paper took use of parameters such as susceptible humans and carrier humans to construct a differential equations model that reasonably depicts the host-to-vector

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Kumar, Abhishek, and Nilam. "Dynamic Behavior of an SIR Epidemic Model along with Time Delay; Crowley–Martin Type Incidence Rate and Holling Type II Treatment Rate." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 7-8 (2019): 757–71. http://dx.doi.org/10.1515/ijnsns-2018-0208.

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Abstract In this article, we propose and analyze a time-delayed susceptible–infected–recovered (SIR) mathematical model with nonlinear incidence rate and nonlinear treatment rate for the control of infectious diseases and epidemics. The incidence rate of infection is considered as Crowley–Martin functional type and the treatment rate is considered as Holling functional type II. The stability of the model is investigated for the disease-free equilibrium (DFE) and endemic equilibrium (EE) points. From the mathematical analysis of the model, we prove that the model is locally asymptotically stabl

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Resmawan, Resmawan, and Lailany Yahya. "Sensitifity Analysis of Mathematical Model of Coronavirus Disease (COVID-19) Transmission." CAUCHY 6, no. 2 (2020): 91. http://dx.doi.org/10.18860/ca.v6i2.9165.

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<span class="fontstyle0">The study was aimed to introduce a new model construction regarding the transmission of Coronavirus Disease (henceforth, COVID-19) in human population. The mathematical model was constructed by taking into consideration several epidemiology parameters that are closely identical with the real condition. The study further conducted an analysis on the model by identifying the endemicity parameters of COVID-19, i.e., the presence of disease-free equilibrium (DFE) point and basic reproduction number. The next step was to carry out sensitivity analysis to find out whic

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Edogbanya, Helen O., Anselm O. Oyem, John O. Dominic, and Jessica M. Gyegwe. "Dynamics of Hepatitis B Virus Disease with Infectious Latent and Vertical Transmission." WSEAS TRANSACTIONS ON BIOLOGY AND BIOMEDICINE 21 (April 16, 2024): 178–91. http://dx.doi.org/10.37394/23208.2024.21.19.

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Hepatitis B has become a major health threat because it is a life-threatening liver disease with an estimated 0.25 billion people suffering from this infectious disease worldwide. This paper presents a SLITR (Susceptible-Latent-Infectious-Treatment-Recovery) mathematical model that combines both vaccination and treatment as a means of controlling the hepatitis B virus (HBV). The nonlinear ordinary differential equations for the HBV transmission capacities were resolved and the basic reproduction number R0 computed using the next generation matrix method and simulated numerically using the Rung

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Duru, Emmanuel Chidiebere, Michael C. Anyanwu, and Mbah Godwin Christopher Ezike. "A mathematical model to investigate the effect of misdiagnosis and wrong treatment in the co-circulation and co-infection of Malaria and Zika virus disease." Bulletin of Biomathematics 3, no. 1 (2025): 79–110. https://doi.org/10.59292/bulletinbiomath.1711811.

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Malaria and Zika virus disease are infectious diseases transmitted among humans through the bites of an infectious female Anopheles and Aedes aegypti mosquitoes, respectively. In areas where the two diseases co-circulate, their coinfection is possible. Both diseases exhibit similar characteristic symptoms, hence one can be misdiagnosed as the other. In this work, we use a system of nonlinear ordinary differential equations to present a new model for the coinfection of the two diseases. The dynamics of the individual diseases are also shown. The disease-free equilibrium (DFE) points of the indi

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Espitia Morillo, Cristian Camilo, and João Frederico da Costa Azevedo Meyer. "HIV/AIDS Mathematical Model of Triangle Transmission." Viruses 14, no. 12 (2022): 2749. http://dx.doi.org/10.3390/v14122749.

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In this paper, a mathematical analysis of the HIV/AIDS deterministic model studied in the paper called Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a case study in the previous works preformed by Espitia is performed. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness; the calculus of the basic reproduction number; stationary points such as disease-fr

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Agrawal, Smriti, Nimisha Mishra, and Joydip Dhar. "Analysis of An SEI1I2QRV S Epidemic Infectious Disease Model with Multiple Infection Stages and Virus." Journal of Neonatal Surgery 14, no. 16S (2025): 1016–28. https://doi.org/10.63682/jns.v14i16s.4735.

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In this study, we propose an SEI1I2QRV Smodel for epidemic infec- tious diseases, which simulates the process of virus transmission. The model demonstrates how the virus impacts individuals who are infected. It is a well-established fact that the spread of infectious diseases can contribute to the proliferation of the virus within a susceptible population. One method of managing infectious diseases is to raise the virus-related fatality rate. In order to explain the virus’s growth and decline rates in the susceptible pop- ulation, the suggested model will be examined. We investigate the dynami

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Chukwumela, Adiela, and Davies Iyai. "Effect of Time Delay in the Stability Analysis of Cholera Epidemic-Endemic Disease Model." European Journal of Theoretical and Applied Sciences 2, no. 3 (2024): 281–97. http://dx.doi.org/10.59324/ejtas.2024.2(3).24.

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Cholera as a disease is a kind of acute diarrhea caused by bacteria Vibrio cholerae. A nonlinear delayed mathematical model with environmental factor for the spread of infectious disease cholera is proposed and analyzed. A mathematical model for cholera was improved by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. It is assumed that all susceptible are affected by carrier population density. The model is analyzed by stability theory of differential equations and co

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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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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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Anusha, S., and S. Athithan. "Mathematical modeling of diabetes and its restrain." International Journal of Modern Physics C 32, no. 09 (2021): 2150114. http://dx.doi.org/10.1142/s012918312150114x.

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In this paper, we have developed a mathematical model of diabetes (type-2 diabetes) in a deterministic approach. We have described our model in the population dynamics with four compartments. Namely, Susceptible, Imbalance Glucose Level (IGL), Treatment and Restrain population. Our model exhibits two nonnegative equilibrium points namely Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The expression for the Treatment reproduction number [Formula: see text] is computed. We have proved that the equilibrium points of the model are locally and globally asymptotically stable under some

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Defterli, Ozlem. "Modeling the impact of temperature on fractional order dengue model with vertical transmission." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 10, no. 1 (2020): 85–93. http://dx.doi.org/10.11121/ijocta.01.2020.00862.

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A dengue epidemic model with fractional order derivative is formulated to investigate the effect of temperature on the spread of the vector-host transmitted dengue disease. The model consists of system of fractional order differential equations formulated within Caputo fractional operator. The stability of the equilibrium points of the considered dengue model is studied. The corresponding basic reproduction number R_0 is derived and it is proved that if R_0 < 1, the disease-free equilibrium (DFE) is locally asymptotically stable. L1 method is applied to solve the dengue model numerically. F

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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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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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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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Lamis, Atikah, and Hengki Tasman. "Dynamic analysis of a coinfection model of dengue and asymptomatic and symptomatic COVID-19." ITM Web of Conferences 61 (2024): 01007. http://dx.doi.org/10.1051/itmconf/20246101007.

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The purpose of this paper is to investigate the transmission dynamics of COVID-19 with Dengue coinfection using a mathematical model. The human population was divided into six compartments, while the mosquito population was divided into two sections. The model considers that COVID-19 infection might be symptomatic or asymptomatic. First, we analyzed the dengue infection model. The basic reproduction number of the COVID-19 infection system and the Dengue infection system are used to forecast illness mitigation and persistence (denoted by ℛ0C and ℛ0D respectively). The qualitative examination of

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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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Engida, Habtamu Ayalew, David Mwangi Theuri, Duncan Gathungu, John Gachohi, and Haileyesus Tessema Alemneh. "A Mathematical Model Analysis for the Transmission Dynamics of Leptospirosis Disease in Human and Rodent Populations." Computational and Mathematical Methods in Medicine 2022 (September 17, 2022): 1–23. http://dx.doi.org/10.1155/2022/1806585.

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This work is aimed at formulating and analyzing a compartmental mathematical model to investigate the impact of rodent-born leptospirosis on the human population by considering a load of pathogenic agents of the disease in an environment and the incidence rate of human infection due to the interaction between infected rodents and the environment. Firstly, the basic properties of the model, the equilibria points, and their stability analysis are studied. We also found the basic reproduction number R 0 of the model using the next-generation matrix approach. From the stability analysis, we obtain

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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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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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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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