Article
Engineering, Mechanical
A. Tanvi, Rajiv Aggarwal, Yashi A. Raj
Summary: In this article, a novel fractional order model is introduced for HIV-TB co-infection to incorporate the memory effect of both diseases. The analysis of both HIV and TB sub-models shows the stability of disease-free equilibrium points and the existence of endemic equilibrium points. Numerical simulations confirm the role of fractional order in co-infection modeling. Memory effect plays a significant role in reducing infection prevalence and increasing the number of recovered individuals when introduced in the fractional order model.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Dawit Denu, Sedar Ngoma, Rachidi B. Salako
Summary: The study focused on the impact of education dissemination on an HIV/AIDS epidemic model, showing that the disease will be eradicated if the basic reproduction number is less than or equal to one, and will be permanent if it is greater than one, with the impact on the population minimized as education dissemination increases. The size of the infected population at the endemic equilibrium decreases linearly with the amount of information disseminated, indicating the importance of education in controlling the disease.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Houjun Liang, Lian Shi, Qizhi He
Summary: This paper discusses the complex dynamics of the Kopel model with nonsymmetric response. The research shows that the fixed point of the nonsymmetric model may undergo various bifurcations under specific parameter combinations. The research also reveals that the effects from rivals can lead to more complex dynamics compared to self-adjustment.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Parvaiz Ahmad Naik, Zohreh Eskandari, Anotida Madzvamuse, Zakieh Avazzadeh, Jian Zu
Summary: This paper investigates different types of bifurcations in a discrete-time seasonally forced SIR epidemic model with a nonstandard discretization scheme. While previous numerical studies have suggested chaotic dynamics in this model, the focus on bifurcation theory has been limited. Analytical and numerical proof is provided for the existence of one and two parameters bifurcations, as well as flip, Neimark-Sacker, and strong resonance bifurcations. The model's complete complex dynamical behavior is explored using a novel technique called nonstandard finite difference discretization scheme (NSFD), and graphical representations are shown to verify the obtained results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Chandan Jana, Atasi Patra Maiti, Dilip Kumar Maiti
Summary: We propose an eco-epidemiological model to study the disease dynamics in a prey-predator system. The model incorporates the spread of disease in the prey population and the recovery of the infected prey through natural immunity. Two time delays, incidence delay and gestation delay, are introduced to account for the conversion of susceptible prey into infected ones and the predator growth. Mathematical requirements and numerical simulations are used to analyze the model behavior and explore the population dynamics under different scenarios.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Bo Li, Yue Zhang, Xiaoliang Li, Zohreh Eskandari, Qizhi He
Summary: This paper presents a novel type of generalized Kopel triopoly model to reveal the complex dynamics and transitions between different dynamic behaviors. The construction process of the model is explained in detail based on microeconomic theory. The existence and stability of fixed points are derived and the corresponding transition processes are presented clearly for some fixed parameters. Numerical simulations are conducted to derive representative orbits, chaotic indicators, Lyapunov exponents, and bifurcation continuation, revealing the complexity of the Kopel triopoly game and corresponding mechanisms.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Mechanical
Soufiane Bentout, Salih Djilali, Tarik Mohammed Touaoula, Anwar Zeb, Abdon Atangana
Summary: In this study, a double age dependence SIRS model is analyzed, focusing on the influence of the incubation period and the immunity period on the outbreak of contagious disease. The study examines the different behaviors generated by these periods in the dynamical system, with a particular emphasis on Hopf bifurcation and the global behavior of solutions using a suitable Lyapunov functional. Additionally, the duration of the incubation period is expected to have a significant impact on the basic reproduction number R-0, which can be considered as a control factor for the outbreak of the infectious disease. Numerical results are checked and represented graphically.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Madhab Barman, Nachiketa Mishra
Summary: This article considers a time delay networked Susceptible-Infectious-Recovered (SIR) epidemic model with a nonlinear incidence rate on a graph of Laplacian diffusion. The model incorporates population mobility through the graph network. Several stability theorems are established for all possible equilibrium points of the model. In addition, Hopf bifurcation analysis is conducted for the endemic equilibrium. Numerical results are provided to validate the theoretical findings.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Engineering, Mechanical
Tangjuan Li, Yanni Xiao
Summary: This study investigates the effects of media coverage and medical resources on disease transmission during the outbreak of emerging infectious diseases. Through the use of a mathematical model and theoretical and numerical analyses, it is found that the limitation of medical resources leads to complex dynamics in the transmission of the virus. Additionally, it is observed that saturated media coverage has little impact on the dynamics. It is suggested that providing adequate medical resources and improving media response measures can help reduce the number of infections.
NONLINEAR DYNAMICS
(2022)
Article
Mathematical & Computational Biology
Fang Zhang, Wenzhe Cui, Yanfei Dai, Yulin Zhao
Summary: This paper investigates the bifurcations of an SIRS epidemic model with a general saturated incidence rate. It shows that the model can undergo various bifurcations for p > 1. These results also improve upon previous findings for a specific case.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Reny George, Nadia Gul, Anwar Zeb, Zakieh Avazzadeh, Salih Djilali, Shahram Rezapour
Summary: This paper presents a discrete-time SIR epidemic model and investigates the stability of its fixed points, as well as the bifurcations of the one and two parameters. Bifurcations such as Neimark-Sacker transcritical, flip, and strong resonance are observed in this model. The MATLAB package MatContM is used to verify the analytical results.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Zohreh Eskandari, Zakieh Avazzadeh
Summary: This study examines the stability and local bifurcations of a discrete-time SIR epidemic model analytically and numerically. Various bifurcations, including transcritical, flip, Neimark-Sacker, and strong resonances, are studied. The obtained analytical results are confirmed using the numerical continuation method and MATLAB toolbox, which also reveal more complex behaviors of the model.
FRACTAL AND FRACTIONAL
(2022)
Article
Materials Science, Multidisciplinary
K. S. Al-Basyouni, A. Q. Khan
Summary: This paper investigates the local behavior, chaos, and bifurcations of a discrete COVID-19 epidemic model in the interior of R5+. The existence of boundary and interior fixed points is explored for all parametric values, and their behavior is analyzed using linear stability theory. It is found that there is no flip bifurcation at the boundary fixed point, but both flip and hopf bifurcations occur at the interior fixed point. The existence of these bifurcations is explored using explicit criteria. Additionally, chaos in the COVID-19 model is investigated through a feedback control strategy, and the theoretical results are verified numerically.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Sayani Adak, Soovoojeet Jana
Summary: In this study, an SIS epidemic model with arbitrary disease transmission function and treatment control function was considered. The model was analyzed by treating the disease transmission function as both an increasing and decreasing function. To introduce heterogeneity, fuzzy numbers were used for both the disease transmission and treatment functions. The fuzzy expected value of the infected individual was defined and computed, leading to the determination of a fuzzy basic reproduction number. A threshold value was then determined for both cases of the system undergoing a transcritical and backward bifurcation.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics, Applied
Liang Chen, JinRong Wang
Summary: In this paper, we study a delayed adaptive network epidemic model where the rate of demographic change of susceptible and infected individuals is affected by the time-delay effects of local spatial connections. We prove the Hopf bifurcation occurs at the critical value t 0 with delay t as the bifurcation parameter. The criteria for the bifurcation direction and stability are derived using the normal form method and central manifold theory. Numerical simulations are provided to demonstrate the feasibility of the results.
Article
Multidisciplinary Sciences
Abdulaziz Y. A. Mukhtar, Justin B. Munyakazi, Rachid Ouifki, Allan E. Clark
Article
Mathematical & Computational Biology
Joseph Malinzi, Rachid Ouifki, Amina Eladdadi, Delfim F. M. Torres, K. A. Jane White
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2018)
Article
Biology
Evans K. Afenya, Rachid Ouifki, Suneel D. Mundle
JOURNAL OF THEORETICAL BIOLOGY
(2019)
Article
Biology
Gideon A. Ngwa, Miranda Teboh-Ewungkem, Yves Dumont, Rachid Ouifki, Jacek Banasiak
JOURNAL OF THEORETICAL BIOLOGY
(2019)
Editorial Material
Medicine, General & Internal
Peter D. Ghys, Brian G. Williams, Mead Over, Timothy B. Hallett, Peter Godfrey-Faussett
Article
Biology
Abdulaziz Y. A. Mukhtar, Justin B. Munyakazi, Rachid Ouifki
MATHEMATICAL BIOSCIENCES
(2019)
Article
Mathematical & Computational Biology
Doreen Mbabazi Ssebuliba, Rachid Ouifki
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2019)
Article
Mathematical & Computational Biology
Kassahun Workalemahu Gashaw, Semu Mitiku Kassa, Rachid Ouifki
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2019)
Article
Biology
Abdulaziz Y. A. Mukhtar, Justin B. Munyakazi, Rachid Ouifki
MATHEMATICAL BIOSCIENCES
(2020)
Article
Multidisciplinary Sciences
Khaphetsi Joseph Mahasa, Lisette de Pillis, Rachid Ouifki, Amina Eladdadi, Philip Maini, A-Rum Yoon, Chae-Ok Yun
SCIENTIFIC REPORTS
(2020)
Article
Mathematics, Applied
Rachid Ouifki, Jacek Banasiak
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2020)
Article
Biology
Noma Susan Senekal, Khaphetsi Joseph Mahasa, Amina Eladdadi, Lisette de Pillis, Rachid Ouifki
Summary: This study investigates the impact of NK cell recruitment to the tumor microenvironment on oncolytic virotherapy. The model developed presents the importance of timing of NK cell responses during oncolytic virotherapy, and predicts that NK cell recruitment influences tumor growth and the likelihood of tumor escape during treatment. The results suggest that a balance between NK responses and viral cytopathicity is crucial for successful oncolytic virotherapy.
BULLETIN OF MATHEMATICAL BIOLOGY
(2021)
Article
Mathematics, Applied
Woldegebriel Assefa Woldegerima, Rachid Ouifki, Jacek Banasiak
Summary: This study develops a population-level compartmental model of human-mosquito interactions considering the use of TBDs for intervention. Mathematical analysis reveals forward and backward bifurcation in the model under certain conditions. The results suggest that the impact of treatment rate on reducing reproduction number depends on key parameters, and effective use of TBDs can significantly reduce malaria deaths.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Biology
Rachid Ouifki, Segun Oke
Summary: Estrogen has a paradoxical role in breast cancer, as it stimulates its growth but also has therapeutic effects. Short-term treatment with estrogen can eliminate breast cancer, but long-term treatment can lead to cancer recurrence. Studies have shown a clinical correlation between estrogen and the p53 protein, which is involved in breast cancer suppression. This research investigates how the interaction between estrogen and p53 affects the dynamics of breast cancer and provides insights into the estrogen paradox and paradoxical tumor recurrence caused by long-term estrogen treatment.
JOURNAL OF MATHEMATICAL BIOLOGY
(2022)
Article
Multidisciplinary Sciences
Christopher Dye, Russell C. H. Cheng, John S. Dagpunar, Brian G. Williams
ROYAL SOCIETY OPEN SCIENCE
(2020)
