Research

18 pages, 44754 KiB

Open AccessArticle

Erlang-Distributed SEIR Epidemic Models with Cross-Diffusion

by Victoria Chebotaeva and Paula A. Vasquez

Mathematics 2023, 11(9), 2167; https://0-doi-org.brum.beds.ac.uk/10.3390/math11092167 - 05 May 2023

Cited by 2 | Viewed by 1362

We explore the effects of cross-diffusion dynamics in epidemiological models. Using reaction–diffusion models of infectious disease, we explicitly consider situations where an individual in a category will move according to the concentration of individuals in other categories. Namely, we model susceptible individuals moving [...] Read more.

We explore the effects of cross-diffusion dynamics in epidemiological models. Using reaction–diffusion models of infectious disease, we explicitly consider situations where an individual in a category will move according to the concentration of individuals in other categories. Namely, we model susceptible individuals moving away from infected and infectious individuals. Here, we show that including these cross-diffusion dynamics results in a delay in the onset of an epidemic and an increase in the total number of infectious individuals. This representation provides more realistic spatiotemporal dynamics of the disease classes in an Erlang

S E I R

model and allows us to study how spatial mobility, due to social behavior, can affect the spread of an epidemic. We found that tailored control measures, such as targeted testing, contact tracing, and isolation of infected individuals, can be more effective in mitigating the spread of infectious diseases while minimizing the negative impact on society and the economy. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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15 pages, 2347 KiB

Open AccessArticle

Mathematical Modelling to Predict the Effect of Vaccination on Delay and Rise of COVID-19 Cases Management

by Charu Arora, Poras Khetarpal, Saket Gupta, Nuzhat Fatema, Hasmat Malik and Asyraf Afthanorhan

Mathematics 2023, 11(4), 821; https://0-doi-org.brum.beds.ac.uk/10.3390/math11040821 - 06 Feb 2023

Cited by 4 | Viewed by 1936

Abstract

In this paper, a mathematical model based on COVID-19 is developed to study and manage disease outbreaks. The effect of vaccination with regard to its efficacy and percentage of population vaccinated in a closed population is investigated. To study virus transmission, the system [...] Read more.

In this paper, a mathematical model based on COVID-19 is developed to study and manage disease outbreaks. The effect of vaccination with regard to its efficacy and percentage of population vaccinated in a closed population is investigated. To study virus transmission, the system employs six nonlinear ordinary differential equations with susceptible–exposed–asymptomatic–infected–vaccinated–recovered populations and the basic reproduction number are calculated. The proposed model describes for highly infectious diseases (such as COVID-19) in a closed containment area with no migration. This paper considers that the percentage of vaccinated population has a significant impact on the number of COVID-19 positive cases during the pandemic wave and examines how the pandemic rise time is delayed. Numerical simulation to investigate disease outbreaks when the community is undergoing vaccination is performed, taking the efficacy rate of the vaccine into account. Sensitivity Index values are calculated for the reproduction number and their relations with few other parameters are depicted. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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15 pages, 840 KiB

Open AccessArticle

Applications of the Delay Stochastic Simulation Algorithm (DSSA) in Mathematical Epidemiology

by Fan Bai

Mathematics 2022, 10(20), 3759; https://0-doi-org.brum.beds.ac.uk/10.3390/math10203759 - 12 Oct 2022

Viewed by 1106

Abstract

The calculation of the probability of a minor outbreak is crucial in analyzing a stochastic epidemic model. For stochastic epidemic models with fixed delays, the linear chain trick is applied to transform the delayed models into a family of ODE models with increasing [...] Read more.

The calculation of the probability of a minor outbreak is crucial in analyzing a stochastic epidemic model. For stochastic epidemic models with fixed delays, the linear chain trick is applied to transform the delayed models into a family of ODE models with increasing shape parameters. We then prove that the well-established results on the probability of a minor outbreak for continuous-time Markov chain (CTMC) epidemic models also hold for the stochastic epidemic models with fixed delays. All theoretical results are verified by numerical simulations implemented by the delay stochastic simulation algorithm (DSSA) in Python. It is shown that DSSA is able to generate exact realizations for underlying delayed models in the context of mathematical epidemiology, and therefore, provides insights into the effect of delays during the outbreak phases of epidemics. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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24 pages, 2367 KiB

Open AccessFeature PaperArticle

Applying Regressive Machine Learning Techniques in Determination of COVID-19 Vaccinated Patients’ Influence on the Number of Confirmed and Deceased Patients

by Sandi Baressi Šegota, Ivan Lorencin, Nikola Anđelić, Jelena Musulin, Daniel Štifanić, Matko Glučina, Saša Vlahinić and Zlatan Car

Mathematics 2022, 10(16), 2925; https://0-doi-org.brum.beds.ac.uk/10.3390/math10162925 - 14 Aug 2022

Cited by 3 | Viewed by 1953

Abstract

Vaccinations are one of the most important steps in combat against viral diseases such as COVID-19. Determining the influence of the number of vaccinated patients on the infected population represents a complex problem. For this reason, the aim of this research is to [...] Read more.

Vaccinations are one of the most important steps in combat against viral diseases such as COVID-19. Determining the influence of the number of vaccinated patients on the infected population represents a complex problem. For this reason, the aim of this research is to model the influence of the total number of vaccinated or fully vaccinated patients on the number of infected and deceased patients. Five separate modeling algorithms are used: Linear Regression (LR), Logistic Regression (LogR), Least Absolute Shrinkage and Selection Operator (LASSO), Multilayer Perceptron (MLP), and Support Vector Regression (SVR). Cross-correlation analysis is performed to determine the optimal lags in data to assist in obtaining better scores. The cross-validation of models is performed, and the models are evaluated using Mean Absolute Percentage Error (MAPE). The modeling is performed for four different countries: Germany, India, the United Kingdom (UK), and the United States of America (USA). Models with an error below 1% are found for all the modeled cases, with the best models being achieved either by LR or MLP methods. The obtained results indicate that the influence of vaccination rates on the number of confirmed and deceased patients exists and can be modeled using ML methods with relatively high precision. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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17 pages, 2246 KiB

Open AccessArticle

Stochastic Modelling of Lassa Fever Epidemic Disease

by Haneen Hamam, Ali Raza, Manal M. Alqarni, Jan Awrejcewicz, Muhammad Rafiq, Nauman Ahmed, Emad E. Mahmoud, Witold Pawłowski and Muhammad Mohsin

Mathematics 2022, 10(16), 2919; https://0-doi-org.brum.beds.ac.uk/10.3390/math10162919 - 13 Aug 2022

Cited by 10 | Viewed by 1582

Abstract

Evolutionary approaches have a critical role in different disciplines such as real-world problems, computer programming, machine learning, biological sciences, and many more. The design of the stochastic model is based on transition probabilities and non-parametric techniques. Positivity, boundedness, and equilibria are investigated in [...] Read more.

Evolutionary approaches have a critical role in different disciplines such as real-world problems, computer programming, machine learning, biological sciences, and many more. The design of the stochastic model is based on transition probabilities and non-parametric techniques. Positivity, boundedness, and equilibria are investigated in deterministic and stochastic senses. An essential tool, Euler–Maruyama, is studied for the solution of said model. Standard and nonstandard evolutionary approaches are presented for the stochastic model in terms of efficiency and low-cost approximations. The standard evolutionary procedures like stochastic Euler–Maruyama and stochastic Runge–Kutta fail to restore the essential features of biological problems. On the other hand, the proposed method is efficient, of meager cost, and adopts all the desired feasible properties. At the end of this paper the comparison section is presented to support efficient analysis. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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18 pages, 1154 KiB

Open AccessArticle

Estimating the Time Reproduction Number in Kupang City Indonesia, 2016–2020, and Assessing the Effects of Vaccination and Different Wolbachia Strains on Dengue Transmission Dynamics

by Meksianis Z. Ndii, Lazarus Kalvein Beay, Nursanti Anggriani, Karolina N. Nukul and Bertha S. Djahi

Mathematics 2022, 10(12), 2075; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122075 - 15 Jun 2022

Cited by 8 | Viewed by 1510

Abstract

The use of a vaccine and Wolbachia bacterium have been proposed as new strategies against dengue. However, the performance of Wolbachia in reducing dengue incidence may depend on the Wolbachia strains. Therefore, in this paper, the performance of two Wolbachia strains which are [...] Read more.

The use of a vaccine and Wolbachia bacterium have been proposed as new strategies against dengue. However, the performance of Wolbachia in reducing dengue incidence may depend on the Wolbachia strains. Therefore, in this paper, the performance of two Wolbachia strains which are WMel and WAu, in combination with the vaccine, has been assessed by using an age-dependent mathematical model. An effective reproduction number has been calculated using the Extended Kalman Filter (EKF) algorithm. The results revealed that the time reproduction number varies overtime with the highest one being around 2.75. Moreover, it has also found that use of the vaccine and Wolbachia possibly leads to dengue elimination. Furthermore, vaccination on one group only reduces dengue incidence in that group but dengue infection in the other group is still high. Furthermore, the performance of the WAu strain is better than the WMel strain in reducing dengue incidence. However, both strains can still be used for dengue elimination strategies depending on the level of loss of Wolbachia infections in both strains. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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9 pages, 2176 KiB

Open AccessArticle

Application of Machine Learning to Study the Association between Environmental Factors and COVID-19 Cases in Mississippi, USA

by Francis Tuluri, Reddy Remata, Wilbur L. Walters and Paul. B. Tchounwou

Mathematics 2022, 10(6), 850; https://0-doi-org.brum.beds.ac.uk/10.3390/math10060850 - 08 Mar 2022

Cited by 1 | Viewed by 1447

Abstract

Because of the large-scale impact of COVID-19 on human health, several investigations are being conducted to understand the underlying mechanisms affecting the spread and transmission of the disease. The present study aimed to assess the effects of selected environmental factors such as temperature, [...] Read more.

Because of the large-scale impact of COVID-19 on human health, several investigations are being conducted to understand the underlying mechanisms affecting the spread and transmission of the disease. The present study aimed to assess the effects of selected environmental factors such as temperature, humidity, dew point, wind speed, pressure, and precipitation on the daily increase in COVID-19 cases in Mississippi, USA, during the period from January 2020 to August 2021. A machine learning model was used to predict COVID-19 cases and implement preventive measures if necessary. A statistical analysis using Python programming showed that the humidity ranged from 56% to 78%, and COVID-19 cases increased from 634 to 3546. Negative correlations were found between temperature and COVID-19 incidence rate (−0.22) and between humidity and COVID-19 incidence rate (−0.15). The linear regression model showed the model linear coefficients to be 0.92 and −1.29, respectively, with the intercept being 55.64. For the test dataset, the R² score was 0.053. The statistical analysis and machine learning show that there is no linear dependence of temperature and humidity with the COVID-19 incidence rate. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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27 pages, 1067 KiB

Open AccessEditor’s ChoiceArticle

Stability and Numerical Solutions of Second Wave Mathematical Modeling on COVID-19 and Omicron Outbreak Strategy of Pandemic: Analytical and Error Analysis of Approximate Series Solutions by Using HPM

by Ashwin Muniyappan, Balamuralitharan Sundarappan, Poongodi Manoharan, Mounir Hamdi, Kaamran Raahemifar, Sami Bourouis and Vijayakumar Varadarajan

Mathematics 2022, 10(3), 343; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030343 - 24 Jan 2022

Cited by 46 | Viewed by 4483

Abstract

This paper deals with the mathematical modeling of the second wave of COVID-19 and verifies the current Omicron variant pandemic data in India. We also we discussed such as uniformly bounded of the system, Equilibrium analysis and basic reproduction number

R_{0}

. [...] Read more.

This paper deals with the mathematical modeling of the second wave of COVID-19 and verifies the current Omicron variant pandemic data in India. We also we discussed such as uniformly bounded of the system, Equilibrium analysis and basic reproduction number

R_{0}

. We calculated the analytic solutions by HPM (homotopy perturbation method) and used Mathematica 12 software for numerical analysis up to 8th order approximation. It checked the error values of the approximation while the system has residual error, absolute error and h curve initial derivation of square error at up to 8th order approximation. The basic reproduction number ranges between

0.8454

and

2.0317

to form numerical simulation, it helps to identify the whole system fluctuations. Finally, our proposed model validated (from real life data) the highly affected five states of COVID-19 and the Omicron variant. The algorithm guidelines are used for international arrivals, with Omicron variant cases updated by the Union Health Ministry in January 2022. Right now, the third wave is underway in India, and we conclude that it may peak by the end of May 2022. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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22 pages, 22876 KiB

Open AccessArticle

Spreading of Infections on Network Models: Percolation Clusters and Random Trees

by Hector Eduardo Roman and Fabrizio Croccolo

Mathematics 2021, 9(23), 3054; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233054 - 28 Nov 2021

Cited by 2 | Viewed by 1976

Abstract

We discuss network models as a general and suitable framework for describing the spreading of an infectious disease within a population. We discuss two types of finite random structures as building blocks of the network, one based on percolation concepts and the second [...] Read more.

We discuss network models as a general and suitable framework for describing the spreading of an infectious disease within a population. We discuss two types of finite random structures as building blocks of the network, one based on percolation concepts and the second one on random tree structures. We study, as is done for the SIR model, the time evolution of the number of susceptible (S), infected (I) and recovered (R) individuals, in the presence of a spreading infectious disease, by incorporating a healing mechanism for infecteds. In addition, we discuss in detail the implementation of lockdowns and how to simulate them. For percolation clusters, we present numerical results based on site percolation on a square lattice, while for random trees we derive new analytical results, which are illustrated in detail with a few examples. It is argued that such hierarchical networks can complement the well-known SIR model in most circumstances. We illustrate these ideas by revisiting USA COVID-19 data. Full article

(This article belongs to the Special Issue Epidemic Models: Track and Control)

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