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Characterizing Chemotherapy-Induced Neutropenia and Monocytopenia Through Mathematical Modelling
In spite of the recent focus on the development of novel targeted drugs to treat cancer, cytotoxic chemotherapy remains the standard treatment for...
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Mathematical Models of Early Hepatitis B Virus Dynamics in Humanized Mice
Analyzing the impact of the adaptive immune response during acute hepatitis B virus (HBV) infection is essential for understanding disease...
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Stability of a general CTL-mediated immunity HIV infection model with silent infected cell-to-cell spread
This paper proposes and analyzes a CTL-mediated HIV infection model. The model describes the interaction between healthy CD4 + T cells, silent infected...
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Optimal Perturbations of Systems with Delayed Independent Variables for Control of Dynamics of Infectious Diseases Based on Multicomponent Actions
In this paper, we apply optimal perturbations to control mathematical models of infectious diseases expressed as systems of nonlinear differential...
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Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?
Several mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the...
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Modelling the Impact of NETosis During the Initial Stage of Systemic Lupus Erythematosus
The development of autoimmune diseases often takes years before clinical symptoms become detectable. We propose a mathematical model for the immune...
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Analysis of Equilibrium Positions for a System that Describes the Interaction of Viruses with the Immune System
We consider a system of two differential equations with respect to the variables that describe the populations of viruses and immune cells....
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Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes
In this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to...
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Mathematical modeling and dynamic analysis of anti-tumor immune response
The competitive interaction of tumor-immune system is very complex. We aim to establish a simple and realistic mathematical model to understand the...
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Modeling tumour heterogeneity of PD-L1 expression in tumour progression and adaptive therapy
Although PD-1/PD-L1 inhibitors show potent and durable anti-tumour effects in some refractory tumours, the response rate in overall patients is...
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Delay Differential Equations with Infectious Diseases
Infectious diseases are among the most prominent threats to mankind. Mathematical modeling of infectious diseases, by using delay differential...
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Implementation of Fractional Optimal Control Problems in Real-World Applications
In this article, we aim to analyze a mathematical model of tumor growth as a problem of fractional optimal control. The considered fractional-order...
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Mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes
Considering that HBV belongs to the DNA virus family and is hepatotropic, we model the HBV DNA-containing capsids as a compartment. In this paper, a...
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Modeling Advanced Immunotherapy with Monoclonal Drugs
In this chapter, applications of monoclonal drugs to control and contain cancer have been studied mathematically. We have used several computer...
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Control Strategies for a Tumor-Immune System with Impulsive Drug Delivery under a Random Environment
This paper mainly studies the stochastic character of tumor growth in the presence of immune response and periodically pulsed chemotherapy. First, a...
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An investigation of tuberculosis progression revealing the role of macrophages apoptosis via sensitivity and bifurcation analysis
Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and latent tuberculosis infection (LTBI)...
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Modelling Cancer Dynamics Using Cellular Automata
Cellular automata and agent-based models have become the cornerstone of the simulation of many complex biological phenomena. More specifically, they...
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Direct Statistical Modeling of HIV-1 Infection Based on a Non-Markovian Stochastic Model
AbstractAn approach to the numerical modeling of the dynamics of HIV-1 infection based on a non-Markovian stochastic model is presented. In the...
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Spatiotemporal Dynamics of a Generalized HBV Infection Model with Capsids and Adaptive Immunity
In this study, we propose and analyze a new mathematical model formulated by partial differential equations in order to better understand the...
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On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies
We review and discuss results obtained through an application of tools of nonlinear optimal control to biomedical problems. We discuss various...
