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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 18195

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Special Issue Editors

Dr. Biao Tang

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Guest Editor

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
Interests: mathematic biology; infectious disease dynamics; nonlinear dynamics; big data analysis in medicine and public health

Dr. Xia Wang

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Guest Editor

School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China
Interests: infectious disease dynamics; statistical data analysis; big data

Special Issue Information

Dear Colleagues,

The importance of mathematical modelling approaches for understanding and controlling major diseases, including communicable and non-communicable diseases, is widely accepted. Mathematical models play an increasingly important role in the prediction and early warning of emerging infectious disease outbreaks or developments in non-communicable diseases, optimizing non-pharmaceutical interventions, therapeutic strategies, and so on. We believe that modelers can make substantial contributions to innovating modelling and analysis methods, providing a better understanding of the dynamic mechanisms of complex biological systems, and helping to solve the current major issues in biomedicine. For this reason, we have initiated a Special Issue focusing on new developments in the fast-growing field of mathematical models of complex biological systems. Potential topics include—but are not limited to—the following:

Mathematical modelling and analysis to understand complex biological systems;
Dynamic mechanism of complex biological systems;
Optimization and control for complex biological systems;
Data-driven modeling of complex biological systems;
Machine learning approaches to biological systems;
Advanced computational methods and data science for biology and biomedicine, etc.

Dr. Biao Tang
Dr. Xia Wang
Guest Editors

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Keywords

infectious disease modelling
epidemiological dynamics
piecewise dynamic systems
optimal control in COVID-19
human behaviours evolution dynamics
data-driven modelling
modelling non-communicable diseases
machine learning approaches

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Published Papers (11 papers)

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Research

22 pages, 387 KiB

Open AccessArticle

Epidemic Models with Varying Infectivity on a Refining Spatial Grid—I—The SI Model

by Anicet Mougabe-Peurkor, Étienne Pardoux and Ténan Yeo

Mathematics 2024, 12(18), 2826; https://doi.org/10.3390/math12182826 - 12 Sep 2024

Viewed by 407

Abstract

We consider a space–time SI epidemic model with infection age dependent infectivity and non-local infections constructed on a grid of the torus

T^{d} = {[0, 1)}^{d}

, where the individuals may migrate from node to node. The migration [...] Read more.

We consider a space–time SI epidemic model with infection age dependent infectivity and non-local infections constructed on a grid of the torus

T^{d} = {[0, 1)}^{d}

, where the individuals may migrate from node to node. The migration processes in either of the two states are assumed to be Markovian. We establish a functional law of large numbers by letting the initial approximate number of individuals on each node, N, to go to infinity and the mesh size of the grid,

ε

, to go to zero jointly. The limit is a system of parabolic PDE/integral equations. The constraint on the speed of convergence of the parameters N and

ε

is that

N ε^{d} \to \infty

(N, ε) \to (+ \infty, 0)

. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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13 pages, 2744 KiB

Open AccessArticle

Estimating Cross-Border Mobility from the Difference in Peak Timing: A Case Study of Poland–Germany Border Regions

by Abhishek Senapati, Adam Mertel, Weronika Schlechte-Welnicz and Justin M. Calabrese

Mathematics 2024, 12(13), 2065; https://doi.org/10.3390/math12132065 - 1 Jul 2024

Viewed by 732

Abstract

Human mobility contributes to the fast spatiotemporal propagation of infectious diseases. During an outbreak, monitoring the infection on either side of an international border is crucial as cross-border migration increases the risk of disease importation. Due to the unavailability of cross-border mobility data, mainly during pandemics, it becomes difficult to propose reliable, model-based strategies. In this study, we propose a method for estimating commuting-type cross-border mobility flux between any pair of regions that share an international border from the observed difference in their infection peak timings. Assuming the underlying disease dynamics are governed by a Susceptible–Infected–Recovered (SIR) model, we employ stochastic simulations to obtain the maximum likelihood cross-border mobility estimate for any pair of regions. We then investigate how the estimate of cross-border mobility flux varies depending on the transmission rate. We further show that the uncertainty in the estimates decreases for higher transmission rates and larger observed differences in peak timing. Finally, as a case study, we apply the method to some selected regions along the Poland–Germany border that are directly connected through multiple modes of transportation and quantify the cross-border fluxes from the COVID-19 cases data from 20 February to 20 June 2021. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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16 pages, 491 KiB

Open AccessArticle

A Mechanistic Model for Long COVID Dynamics

by Jacob Derrick, Ben Patterson, Jie Bai and Jin Wang

Mathematics 2023, 11(21), 4541; https://doi.org/10.3390/math11214541 - 3 Nov 2023

Viewed by 1198

Abstract

Long COVID, a long-lasting disorder following an acute infection of COVID-19, represents a significant public health burden at present. In this paper, we propose a new mechanistic model based on differential equations to investigate the population dynamics of long COVID. By connecting long COVID with acute infection at the population level, our modeling framework emphasizes the interplay between COVID-19 transmission, vaccination, and long COVID dynamics. We conducted a detailed mathematical analysis of the model. We also validated the model using numerical simulation with real data from the US state of Tennessee and the UK. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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15 pages, 9673 KiB

Open AccessArticle

Pattern Formation in a Predator–Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks

by Lei Shi, Jiaying Zhou and Yong Ye

Mathematics 2023, 11(15), 3339; https://doi.org/10.3390/math11153339 - 30 Jul 2023

Cited by 3 | Viewed by 1488

Abstract

With the rapid development of network science, Turing patterns on complex networks have attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator–prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing patterns is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing patterns. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing patterns is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing patterns, which are not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing patterns and spatiotemporal patterns. We believe that these findings contribute to a better understanding of self-organization on complex networks. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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37 pages, 5758 KiB

Open AccessArticle

Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish

by Sk Golam Mortoja, Prabir Panja and Shyamal Kumar Mondal

Mathematics 2023, 11(13), 3011; https://doi.org/10.3390/math11133011 - 6 Jul 2023

Cited by 8 | Viewed by 2806

Abstract

Plankton occupy a vital place in the marine ecosystem due to their essential role. However small or microscopic, their absence can bring the entire life process to a standstill. In this work, we have proposed a prey–predator ecological model consisting of phytoplankton, zooplankton, and fish, incorporating the cannibalistic nature of zooplankton harvesting the fish population. Due to differences in their feeding habits, zooplankton are divided into two sub-classes: herbivorous and carnivorous. The dynamic behavior of the model is examined for each of the possible steady states. The stability criteria of the model have been analyzed from both local and global perspectives. Hopf bifurcation analysis has been accomplished with the growth rate of carnivorous zooplankton using cannibalism as a bifurcation parameter. To characterize the optimal control, we have used Pontryagin’s maximum principle. Subsequently, the optimal system has been derived and solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Finally, to facilitate the interpretation of our mathematical results, we have proceeded to investigate it using numerical simulations. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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24 pages, 663 KiB

Open AccessArticle

Bifurcation of an SIRS Model with a Modified Nonlinear Incidence Rate

by Yingying Zhang and Chentong Li

Mathematics 2023, 11(13), 2916; https://doi.org/10.3390/math11132916 - 29 Jun 2023

Cited by 2 | Viewed by 1153

Abstract

An SIRS epidemic model with a modified nonlinear incidence rate is studied, which describes that the infectivity is strong at first as the emergence of a new disease or the reemergence of an old disease, but then the psychological effect will weaken the infectivity. Lastly, the infectivity goes to a saturation state as a result of a crowding effect. The nonlinearity of the functional form of the incidence of infection is modified, which is more reasonable biologically. We analyze the stability of the associated equilibria, and the basic reproduction number and the critical value which determine the dynamics of the model are derived. The bifurcation analysis is presented, including backward bifurcation, saddle-node bifurcation, Bogdanov–Takens bifurcation of codimension two and Hopf bifurcation. To study Hopf bifurcation of codimension three of the model when some assumptions hold, the focus values are calculated. Numerical simulations are shown to verify our results. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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27 pages, 1685 KiB

Open AccessArticle

The Influence of Migration to Regions with Different Coverages of Health Education on Schistosomiasis

by Pan Tang, Shiwen Qian, Lei Shi, Longxing Qi and Tingting Li

Mathematics 2023, 11(12), 2666; https://doi.org/10.3390/math11122666 - 12 Jun 2023

Viewed by 1156

Abstract

Background: Health education plays a vital role in the prevention and control of schistosomiasis in China and throughout the world. However, the coverage of health education varies from place to place for various reasons. Moreover, people with different levels of health education migrate between different regions. Methods: In order to analyze the effects of different coverages of health education on schistosomiasis transmission, a schistosomiasis mathematical model with people’s inter-regional migration is constructed in two regions with different coverages of health education. The basic reproduction number is calculated, the global stability of the system is analyzed qualitatively, and a numerical simulation is carried out. Results: (1) The transmission trend of schistosomiasis could be reduced by increasing the migration of the susceptible population from the region with a high coverage of health education to the region with low coverage, or by increasing the migration of the infected population between the two regions. Schistosomiasis can even be eliminated if the migration of the susceptible or infected population from the region with a high coverage of health education to the region with a low coverage is sufficiently large. This is quite different from the prevention and control of other epidemics in which the movement of people should be restricted. (2) A low coverage of health education will have an impact on the number of patients and infected snails in both of the two regions. This result indicates that increasing the coverage of health education can reduce the risk of schistosomiasis not only in the local population but also in the surrounding regions to which people migrate. Conclusions: There is no need to restrict the migration of the infected population between the two regions nor the migration of the susceptible population from the region with a high coverage of health education to the region with a low coverage. However, there is a need to restrict the migration of the susceptible population from the region with a low coverage of health education to the region with a high coverage. These are some suggestions to prevent and control schistosomiasis. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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18 pages, 628 KiB

Open AccessArticle

Mathematical Analysis of a Bacterial Competition in a Continuous Reactor in the Presence of a Virus

by Abdulrahman Ali Alsolami and Miled El Hajji

Mathematics 2023, 11(4), 883; https://doi.org/10.3390/math11040883 - 9 Feb 2023

Cited by 13 | Viewed by 1668

Abstract

In this paper, we discuss the competition of two species for a single essential growth-limiting nutriment with viral infection that affects only the first species. Although the classical models without viral infection suggest competitive exclusion, this model exhibits the stable coexistence of both species. We reduce the fourth-dimension proposed model to a three-dimension one. Thus, the coexistence of the two competing species is demonstrated using the theory of uniform persistence applied to the three-variable reduced system. We prove that there is no coexistence of both species without the presence of the virus and the satisfaction of some assumptions on the growth rates of species. Finally, we give some numerical simulations to confirm the obtained theoretical findings. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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18 pages, 739 KiB

Open AccessArticle

Bayesian Inference for COVID-19 Transmission Dynamics in India Using a Modified SEIR Model

by Kai Yin, Anirban Mondal, Martial Ndeffo-Mbah, Paromita Banerjee, Qimin Huang and David Gurarie

Mathematics 2022, 10(21), 4037; https://doi.org/10.3390/math10214037 - 31 Oct 2022

Cited by 5 | Viewed by 2139

Abstract

We propose a modified population-based susceptible-exposed-infectious-recovered (SEIR) compartmental model for a retrospective study of the COVID-19 transmission dynamics in India during the first wave. We extend the conventional SEIR methodology to account for the complexities of COVID-19 infection, its multiple symptoms, and transmission pathways. In particular, we consider a time-dependent transmission rate to account for governmental controls (e.g., national lockdown) and individual behavioral factors (e.g., social distancing, mask-wearing, personal hygiene, and self-quarantine). An essential feature of COVID-19 that is different from other infections is the significant contribution of asymptomatic and pre-symptomatic cases to the transmission cycle. A Bayesian method is used to calibrate the proposed SEIR model using publicly available data (daily new tested positive, death, and recovery cases) from several Indian states. The uncertainty of the parameters is naturally expressed as the posterior probability distribution. The calibrated model is used to estimate undetected cases and study different initial intervention policies, screening rates, and public behavior factors, that can potentially strike a balance between disease control and the humanitarian crisis caused by a sudden strict lockdown. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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15 pages, 508 KiB

Open AccessArticle

Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2

by Kaushik Dehingia, Ahmed A. Mohsen, Sana Abdulkream Alharbi, Reima Daher Alsemiry and Shahram Rezapour

Mathematics 2022, 10(13), 2344; https://doi.org/10.3390/math10132344 - 4 Jul 2022

Cited by 21 | Viewed by 1801

Abstract

The prime objective of the current study is to propose a novel mathematical framework under the fractional-order derivative, which describes the complex within-host behavior of SARS-CoV-2 by taking into account the effects of memory and carrier. To do this, we formulate a mathematical model of SARS-CoV-2 under the Caputo fractional-order derivative. We derived the conditions for the existence of equilibria of the model and computed the basic reproduction number

R_{0}

. We used mathematical analysis to establish the proposed model’s local and global stability results. Some numerical resolutions of our theoretical results are presented. The main result of this study is that as the fractional derivative order increases, the approach of the solution to the equilibrium points becomes faster. It is also observed that the value of

R_{0}

increases as the value of

β

and

π_{v}

increases. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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18 pages, 2536 KiB

Open AccessArticle

Epidemic Dynamics of Two-Pathogen Spreading for Pairwise Models

by Shanshan Chen, Yijun Ran, Hebo Huang, Zhenzhen Wang and Ke-ke Shang

Mathematics 2022, 10(11), 1906; https://doi.org/10.3390/math10111906 - 2 Jun 2022

Cited by 6 | Viewed by 2052

Abstract

In the real world, pathogens do not exist in isolation. The transmission of one pathogen may be affected by the presence of other pathogens, and certain pathogens generate multiple strains with different spreading features. Hence, the behavior of multi-pathogen transmission has attracted much attention in epidemiological research. In this paper, we use the pairwise approximation method to formulate two-pathogen models capturing cross-immunity, super-infection, and co-infection phenomena, in which each pathogen follows a susceptible-infected-susceptible (SIS) mechanism. For each model, we calculate the basic reproduction number and analyze the stability of equilibria, and discuss the differences from the mean-field approach. We demonstrate that simulations are in good agreement with the analytical results. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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