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Mathematical Advances in Studying Rare and Novel Diseases

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Dr. Natalia Nikitina

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Guest Editor

Institute of Applied Mathematical Research, Karelian Research Centre of the RAS, 185910 Petrozavodsk, Russia
Interests: volunteer computing; distributed computing; high-performance computing; BOINC; game theory; task scheduling

Dr. Marko Jukić

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Guest Editor

1. Faculty of Chemistry and Chemical Engineering, Laboratory of Physical Chemistry and Chemical Thermodynamics, University of Maribor, 2000 Maribor, Slovenia
2. Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, 6000 Koper, Slovenia
Interests: computational chemistry; combinatorial chemistry in silico; computer-aided drug design; molecular modeling; machine learning

Dr. Črtomir Podlipnik

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Guest Editor

Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1000 Ljubljana, Slovenia
Interests: computational chemistry; combinatorial chemistry in silico; biomolecular systems; drug design; quantum chemical computing; molecular modeling; molecular dynamics simulation; computer-aided drug design

Special Issue Information

Dear Colleagues,

By now, mathematics has contributed many models, methods and algorithms to the fight against human diseases. Mathematical analysis is widely used to control the load on public health systems, to monitor and predict disease spread, to assist drug and vaccine development, and to evaluate and confirm empirical biological methods. Researchers of rare diseases have a specific interest in analytical and computational methods when they deal with limited possibilities of clinical trials. In the fight against novel diseases, of particular importance is an accurate and reliable prediction of disease spread and severity. Under epidemiological threat, the challenge is to develop a quick response including the discovery of drugs and vaccines under the conditions of an intrinsic lack of biomedical data for analysis.

In this Special Issue, we aim to gather new and unpublished works on mathematical advances targeting research of rare and novel diseases. We welcome mathematical models, computational algorithms and other contributions to this interdisciplinary area with a strong mathematical basis.

Dr. Natalia Nikitina
Dr. Marko Jukić
Dr. Črtomir Podlipnik
Guest Editors

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Keywords

rare diseases
novel diseases
statistical modelling
statistical analysis
predictive modeling
predictive analysis
mathematical modelling in epidemiology
machine learning
artificial intelligence
biomathematics
bioinformatics

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Research

26 pages, 1769 KiB

Open AccessArticle

Global Dynamics of Viral Infection with Two Distinct Populations of Antibodies

by Ahmed M. Elaiw, Aeshah A. Raezah and Matuka A. Alshaikh

Mathematics 2023, 11(14), 3138; https://doi.org/10.3390/math11143138 - 16 Jul 2023

Viewed by 921

Abstract

This paper presents two viral infection models that describe dynamics of the virus under the effect of two distinct types of antibodies. The first model considers the population of five compartments, target cells, infected cells, free virus particles, antibodies type-1 and antibodies type-2. The presence of two types of antibodies can be a result of secondary viral infection. In the second model, we incorporate the latently infected cells. We assume that the antibody responsiveness is given by a combination of the self-regulating antibody response and the predator–prey-like antibody response. For both models, we verify the nonnegativity and boundedness of their solutions, then we outline all possible equilibria and prove the global stability by constructing proper Lyapunov functions. The stability of the uninfected equilibrium

{EQ}^{0}

and infected equilibrium

{EQ}^{*}

is determined by the basic reproduction number

R_{0}

. The theoretical findings are verified through numerical simulations. According to the outcomes, the trajectories of the solutions approach

{EQ}^{0}

and

{EQ}^{*}

when

R_{0} \leq 1

and

R_{0} > 1

, respectively. We study the sensitivity analysis to show how the values of all the parameters of the suggested model affect

R_{0}

under the given data. The impact of including the self-regulating antibody response and latently infected cells in the viral infection model is discussed. We showed that the presence of the self-regulating antibody response reduces

R_{0}

and makes the system more stabilizable around

{EQ}^{0}

. Moreover, we established that neglecting the latently infected cells in the viral infection modeling leads to the design of an overflow of antiviral drug therapy. Full article

(This article belongs to the Special Issue Mathematical Advances in Studying Rare and Novel Diseases)

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20 pages, 729 KiB

Open AccessArticle

Effect of Antiviral Therapy for HCV Treatment in the Presence of Hepatocyte Growth Factor

by Santosh Kumar Sharma, Amar Nath Chatterjee and Bashir Ahmad

Mathematics 2023, 11(3), 751; https://doi.org/10.3390/math11030751 - 02 Feb 2023

Cited by 1 | Viewed by 1153

Abstract

The effect of antiviral therapy during Hepatitis C Virus (HCV) infection is the focus of this study. HCV infection destroys healthy hepatocyte cells in the human liver, causing cirrhosis and hepatocellular carcinoma. We introduce a cell-population model representing the long-term dynamics of HCV infection in response to antiviral drug therapies. The proliferation of existing cells can create hepatocyte cells in the system. Such models are based on the dynamics of susceptible hepatocytes, infected hepatocytes and HCV with interactive dynamics, which can give a complete understanding of the host dynamics of the system in the presence of antiviral drug therapy. Infection-free equilibrium and endemic equilibrium are two equilibrium states in the absence of drugs. The existence and stability conditions for both systems are presented. We also construct an optimal control system to find the optimal control strategy. Numerical results show that the effects of the proliferation rate and infection rate are critical for the changes in the dynamics of the model. The impact of different weight factors on the optimal control problem is analysed through numerical simulation. Full article

(This article belongs to the Special Issue Mathematical Advances in Studying Rare and Novel Diseases)

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