Bulletin of Biomathematics

A fractional-order model of COVID-19 and Malaria co-infection

Livinus Loko Iwa — 2024-10-31

This paper explores the co-infection dynamics of coronavirus disease 2019 (COVID-19) and Malaria using Caputo-type fractional derivative to further understand the disease interactions and implement effective control strategies. We demonstrate the positivity and boundedness of the solution through Laplace transform techniques and establish the existence and uniqueness of the solution, showcasing model stability using fractional-order stability theory. Simulation experiments across varying fractional orders and disease classes offer insights into the co-infection dynamics. This is a new model and the findings underscore the potential impact of control measures on mitigating co-infection under endemic conditions. We conclude that infection with malaria does not guarantee immunity to COVID-19 and infection with COVID-19 as well does not guarantee immunity to malaria.

A stochastic approach to tumor modeling incorporating macrophages

Sümeyra Uçar — 2024-10-31

Macrophages are essential components of the immune system’s response to tumors, engaging in intricate interactions shaped by factors such as tumor type, progression, and the surrounding microenvironment. These dynamic relationships between macrophages and cancer cells have become a focal point of research, as scientists seek innovative ways to harness the immune system, including macrophages, for cancer immunotherapy. In this study, we introduce a novel model that examines the interaction between tumor and macrophage cells. We provide an in-depth analysis of the equilibrium points and their stability, as well as a thorough investigation into the solution properties of the model. Moreover, by incorporating a stochastic approach, we account for inherent randomness and fluctuations within the system, offering a more comprehensive understanding of tumor-immune dynamics. Numerical simulations further validate the model, providing key insights into how stochastic elements may influence tumor progression and immune response.

Bifurcations on a discrete–time SIS–epidemic model with saturated infection rate

Hasan S. Panigoro — 2024-10-31

In this paper, we explore the complex dynamics of a discrete-time SIS (Susceptible-Infected-Susceptible)-epidemic model. The population is assumed to be divided into two compartments: susceptible and infected populations where the birth rate is constant, the infection rate is saturated, and each recovered population has a chance to become infected again. Two types of mathematical results are provided namely the analytical results which consist of the existence of fixed points and their dynamical behaviors, and the numerical results, which consist of the global sensitivity analysis, bifurcation diagrams, and the phase portraits. Two fixed points are obtained namely the disease-free and the endemic fixed points and their stability properties. Some numerical simulations are provided to present the global sensitivity analysis and the existence of some bifurcations. The occurrence of forward and period-doubling bifurcations has confirmed the complexity of the solutions.

The effect of amyloid beta, membrane, and ER pathways on the fractional behavior of neuronal calcium

Brajesh Kumar Jha — 2024-10-31

Calcium signal transduction is essential for cellular activities such as gene transcription, death, and neuronal plasticity. Dynamical changes in the concentration of calcium have a profound effect on the intracellular activity of neurons. The Caputo fractional reaction-diffusion equation is a useful tool for modeling the intricate biological process involved in calcium concentration regulation. We include the Amyloid Beta, STIM-Orai mechanism, voltage-dependent calcium entry, inositol triphosphate receptor (IPR), endoplasmic reticulum (ER) flux, SERCA pump, and plasma membrane flux in our mathematical model. We use Green's function and Hankel and Laplace integral transforms to solve the membrane flux problem. Our simulations investigate the effects of various factors on the spatiotemporal behavior of calcium levels, with a simulation on the buffers in Alzheimer's disease-affected neurons. We also look at the effects of calcium-binding substances like the S100B protein and BAPTA and EGTA. Our results demonstrate how important the S100B protein Amyloid beta and the STIM-Orai mechanism are, and how important they are to consider when simulating the calcium signaling system. As such, our research indicates that a more realistic and complete model for modeling calcium dynamics may be obtained by using a generalized reaction-diffusion technique.

A mathematical model for the study of HIV/AIDS transmission with PrEP coverage increase and parameter estimation using MCMC with a Bayesian approach

Erick Manuel Delgado Moya — 2024-10-31

In this article, we present a mathematical model for the study of HIV/AIDS considering the implementation of Pre-Exposure Prophylaxis (PrEP). As a novel element in the construction of the model, we consider the diagnosis of cases for attempting to enter the PrEP program, which allows us to study different forms of PrEP. The diagnosis of new infections helps to reduce transmission in the population because these patients are incorporated into the therapy and can achieve an undetectable viral load in blood which prevents them from infecting others. The model contains a compartment of infected persons with undetectable viral load in blood that is reached by adherence to treatment which is separated from those simply infected with the virus as they do not transmit it. Considering the structure of the model, we propose a method to study the effect of increased PrEP use and HIV incidence in a population. In the case of incidence, we took into account the stochasticity of the behavior. Besides, we find the basic reproduction number and present results that allow us to obtain the impact of the parameters associated with transmission, treatment and diagnosis on the basic reproduction number. We perform computational simulations, using demographic and HIV/AIDS data from Brazil, and utilize the Markov Chain Monte Carlo (MCMC) method with a Bayesian approach to estimate model parameters. We study two coverage increases at 25% and 35% that were selected according to the size of the Brazilian population and the daily use of PrEP. We compare the increases in coverage focused on HIV incidence, which is the number of new HIV cases infected and the number of HIV cases avoided, we conclude that by increasing PrEP coverage the incidence of HIV is reduced and the number of cases avoided increases.