Volume 13, Issue 1

This article explores how emotional feelings linked to stored memories of past experiences influence the present activity of the human brain. To analyse this, a mathematical model is considered describing the dynamics in a two-layered network in which the neurons in the first layer are involved in present activities and are influenced by cells in the second layer that carry the emotional feelings associated with memories of past experiences. Initially, this article establishes sufficient conditions for the stability of a unique equilibrium solution in the system for both constant and time-varying exogenous inputs. This indicates the situation where the present activities are not disturbed by emotions emanated from past memories. Furthermore, it is observed that certain variations in the exogenous inputs can induce oscillations within the system. To manage them, this study suggests the adjustment of specific parameters that could actually control certain fluctuations according to emotional responses to past and current memories. This control aims to stabilize the brain’s current activity, allowing it to reach a balanced state.

This study examines the impact of measurement errors on parameter estimates within hierarchical Bayesian semiparametric (HBS) models, with a focus on the Lotka–Volterra predator–prey model as a case study. By employing Gibbs sampling within the Markov Chain Monte Carlo framework, we simulate various levels of measurement errors to assess the robustness of these models. Results indicate that HBS models effectively account for measurement error, mitigating its adverse effects on the accuracy of parameter estimates, especially for complex, nonlinear systems like predator–prey dynamics. The study demonstrates that as sample sizes increase, the models’ ability to recover true population interaction parameters, such as prey birth rates and predator consumption rates, improves significantly. These findings underscore the importance of using advanced Bayesian methods to correct for measurement errors, ensuring reliable statistical inferences in fields like ecological modeling, environmental studies, and agricultural systems. The integration of HBS models enhances the reliability of complex data analyses, providing essential insights into nonlinear interactions in real-world systems.

This study aims to enhance coronavirus disease 2019 forecasting in Kenya by comparing the predictive performance of statistical, machine learning, and deep learning (DL) models for total cases, critical cases, severe cases, and total deaths, using data from April 2020 to August 2021. Six models – autoregressive integrated moving average (ARIMA), support vector regression, random forest (RF), recurrent neural network, long short-term memory, and gated recurrent unit – were evaluated with an 80–20 train-test split, employing root mean squared error, mean absolute error, mean absolute percentage error, and R 2 {R}^{2} metrics. The Diebold-Mariano (DM) test assessed statistical significance of error differences. Results reveal RF as the top performer, consistently achieving the lowest errors and highest R 2 {R}^{2} across all datasets, indicating superior accuracy in capturing nonlinear epidemic patterns. GRU outperformed other DL models, while ARIMA showed the weakest performance. The DM test confirmed significant differences in forecasting errors, with RF generally outperforming other models.

When planktonic bacteria adhere together to a surface, they begin to form biofilms, communities of bacteria. Biofilm formation in a host can be extremely problematic if left untreated, especially since antibiotics can be ineffective in treating the bacteria. Certain lung diseases such as cystic fibrosis can cause the formation of biofilms in the lungs and can be fatal. With antibiotic-resistant bacteria, the use of phage therapy has been introduced as an alternative or an additive to the use of antibiotics to combat biofilm growth. Phage therapy utilizes bacteriophages that attack bacteria, to penetrate and eradicate biofilms. To evaluate the effectiveness of phage therapy against biofilm bacteria, we create a phage-biofilm model with ordinary differential equations and a stochastic model. We considered three possible cases for the stability of disease-free equilibrium; by model simulations and parameter alterations in both models, we investigated the effect of bacteria–phage interactions alongside biofilm bacteria cell detachment from the biofilm phase to the planktonic phase, and how these will affect the efficiency of phage therapy against bacteria. Our results show that, by increasing the phage mortality rate, the biofilm growth can be balanced, which makes it more vulnerable to antibiotics. Thus, phage therapy is an effective aid in biofilm treatment.

Understanding the dynamics of infectious diseases using mathematical modeling is essential for developing prevention and control measures. Hepatitis B is still a major public health issue in many places, including Kenya, where the high incidence of illness presents serious difficulties. In this article, the existence and uniqueness of solutions for a fractional hepatitis B model in the Caputo sense were explored. Furthermore, using the Adams-type Predictor-Corrector method, numerical simulations of the fractional order model are carried out. The outcomes show how well the suggested control strategies work to stop the spread of hepatitis B virus.

This study presents a mathematical model of glioma growth dynamics with drug resistance, capturing interactions among five cell populations – glial cells, sensitive and resistant glioma cells, endothelial cells, and neurons – alongside chemotherapy and antiangiogenic therapy. Glioma, a malignant tumor originating in glial cells, undergoes chemotherapy-induced mutations, leading to drug-resistant variants that affect both tumor and normal cells. The model incorporates a Holling Type II response function to optimize treatment doses while inducing angiogenic dormancy. Stability analysis identifies three equilibrium points – two stable and one unstable – while numerical simulations using phase portraits and trajectory diagrams illustrate the impact of combined therapies. This model provides insights into glioma progression and drug resistance, emphasizing the efficacy of combined therapies for optimizing treatment strategies.

Recent studies have intensified the risk of post-COVID-19 cardiovascular diseases. In an effort to understand the intricate dynamics of COVID-19 infection, this article suggests a four-compartment model to portray the dynamic interplay between the susceptible population, the COVID-19-infected population detected without and with cardiovascular disease, and the recovered population. Basic properties such as nonnegativity and boundedness of solutions and the existence of disease-free and endemic equilibria are discussed. The model’s basic reproduction number is obtained. Sufficient conditions for local and global stability at the equilibrium point are established by restricting the functionals and parameters of the system. Numerical examples are illustrated to support the results. The relative significance of the model parameters to disease transmission is determined by performing a sensitivity analysis of the model. It is found that a rise in infection among the cardio population will drastically affect the overall infection rate compared to that of the noncardio population, supporting the real-time scenario. This model also emphasizes the importance of vaccination and treatment in controlling the spread of the virus.

In this article, we study a fractional-order prey-predator model incorporating prey refuge and predator harvesting, employing a Holling type III functional response. The model’s dynamics are explored using the consumption number C 0 {C}_{0} , providing a comprehensive understanding of its ecological implications. We establish the existence and uniqueness of the solution, ensuring the model’s mathematical robustness. Stability analysis is conducted to determine the conditions under which the system remains in equilibrium. Sensitivity analysis is performed to assess the importance of various parameters on the system’s behaviour with respect to the consumption number. Additionally, we investigate the occurrence of transcritical bifurcations, utilizing the prey refuge as a bifurcation parameter. Numerical simulations are carried out to illustrate the theoretical results and to provide deeper insights into the model’s dynamics. Our findings contribute to the understanding of fractional-order systems in ecological modelling and offer valuable perspectives on the management of predator-prey interactions in the presence of prey refuge and predator harvesting.

This study explores the dynamic characteristics of a fractional-order model for the hepatitis B virus (HBV) epidemic. We present the existence, uniqueness, and Ulam-Hyers stability of solutions for a fractional-order HBV model utilizing the Atangana-Baleanu-Caputo fractional operator with Mittag-Leffler kernels. For the fractional numerical simulations, we employ the Adams-Moulton numerical scheme. The results from the numerical solutions indicate that the parameter χ \chi (order of derivative) plays a crucial role, highlighting the importance of the two infection stages (acute and chronic) within the model. We observed the relationship between the basic reproduction number, the HBV transmission rate, the birth-rate, and the acutely infected individuals to the chronic stage.

Oncolytic virotherapy is one of the cancer treatments that kills cancer cells but leaves normal cells. Furthermore, mitogen-activated protein kinase (MEK) inhibitors boost chimeric antigen receptor expression and increase oncolytic virus entry into tumor cells, and TNF- α {\rm{\alpha }} inhibitors improve the effectiveness of oncolytic virotherapy. We propose a mathematical model of tumor involving oncolytic virotherapy, MEK inhibitors, and TNF- α {\rm{\alpha }} inhibitors. All model properties are performed. Three equilibrium points are computed, and their stabilities are analyzed. Additionally, optimal control is applied to the model to investigate the optimal strategy to reduce the load of tumor cells by using MEK inhibitors, TNF- α {\rm{\alpha }} inhibitors, and oncolytic virotherapy. Numerical results demonstrate that a combination of all three treatments leads to a significant increase in infected tumor cells and macrophages, resulting in more infections of tumor cells and stronger immune response. Both low and high levels of MEK inhibitors are applied in three-treatment combination to explore a role of MEK inhibitors, and a better result in high level of MEK inhibitors case is obtained. Hence, our results confirm that MEK inhibitors could lead to not only more oncolytic virus infection of tumor cells and more immune of macrophages but also limit the virus replication.