Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel

This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractional order model. Additionally, stability is evaluated, along with the local and global effects of the virus that causes Ebola. Using the fractional order model of Ebola virus infections, the existence and uniqueness of solutions, as well the posedness and biological viability and disease free equilibrium points are confirmed. Many applications of fractional operators in modern mathematics exist, including the intricate and important study of symmetrical systems. Symmetry analysis is a powerful tool that enables the creation of numerical solutions for a given fractional differential equation very methodically. For this, we compare the results with the Caputo derivative operator to understand the dynamic behavior of the disease. The simulation demonstrates how all classes have convergent characteristics and maintain their places over time, reflecting the true behavior of Ebola virus infection. Power law kernel with the two step polynomial Newton method were used. This model seems to be quite strong and capable of reproducing the issue’s anticipated theoretical conditions.Basque Government:Grant IT1555-22 Basque Government: Grant KK-2022/00090 MCIN/AEI 269.10.13039/501100011033/FEDER,UE: Grant PID2021-1235430B-C21 MCIN/AEI 269.10.13039/501100011033/FEDER,UE: Grant PID2021-1235430B-C22

A New Efficient Technique for Solving Modified Chua's Circuit Model with a New Fractional Operator

Chua's circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua's circuit is obtained by transforming the classical model of Chua's circuit into novel forms of various fractional derivatives. The new obtained system is then named fractional Chua's circuit model. The modified system is then analyzed by the optimal perturbation iteration method. Illustrations are given to show the applicability of the algorithms, and effective graphics are sketched for comparison purposes of the newly introduced fractional operatorsThe authors are grateful to the Spanish Government for Grant RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE) and to the Basque Government for Grant IT1207-1

Consequences of Short Term Mobility Across Heterogeneous Risk Environments: The 2014 West African Ebola Outbreak

abstract: In this dissertation the potential impact of some social, cultural and economic factors on Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is addressed. A mathematical model, calibrated with data from the 2014 West African outbreak, is used to show the dynamics of EVD control under various quarantine and isolation effectiveness regimes. It is shown that in order to make a difference it must reach a high proportion of the infected population. The effect of EVD-dead bodies has been incorporated in the quarantine effectiveness. In Chapter four, the potential impact of differential risk is assessed. A two-patch model without explicitly incorporate quarantine is used to assess the impact of mobility on communities at risk of EVD. It is shown that the overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed. The cost that individuals in the low-risk patch must pay, as measured by secondary cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine levels is used to show that quarantine a large enough proportion of the population under effective isolation leads to a measurable reduction of secondary cases in the presence of mobility. It is shown that sharing limited resources can improve the effectiveness of EVD effective control in the two-patch high-low risk system. Identifying the conditions under which the low-risk community would be willing to accept the increases in EVD risk, needed to reduce the total number of secondary cases in a community composed of two patches with highly differentiated risks has not been addressed. In summary, this dissertation looks at EVD dynamics within an idealized highly polarized world where resources are primarily in the hands of a low-risk community – a community of lower density, higher levels of education and reasonable health services – that shares a “border” with a high-risk community that lacks minimal resources to survive an EVD outbreak.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Nonlinear growth and mathematical modelling of COVID-19 in some African countries with the Atangana-Baleanu fractional derivative

We analyse the time-series evolution of the cumulative number of confirmed cases of COVID-19, the novel coronavirus disease, for some African countries. We propose a mathematical model, incorporating non-pharmaceutical interventions to unravel the disease transmission dynamics. Analysis of the stability of the model’s steady states was carried out, and the reproduction number R0, a vital key for flattening the time-evolution of COVID-19 cases, was obtained by means of the next generation matrix technique. By dividing the time evolution of the pandemic for the cumulative number of confirmed infected cases into different regimes or intervals, hereafter referred to as phases, numerical simulations were performed to fit the proposed model to the cumulative number of confirmed infections for different phases of COVID-19 during its first wave. The estimated R0 declined from 2.452 – 9.179 during the first phase of the infection to 1.374 – 2.417 in the last phase. Using the Atangana-Baleanu fractional derivative, a fractional COVID-19 model is proposed and numerical simulations performed to establish the dependence of the disease dynamics on the order of the fractional derivatives. An elasticity and sensitivity analysis of R0 was carried out to determine the most significant parameters for combating the disease outbreak. These were found to be the effective disease transmission rate, the disease diagnosis or case detection rate, the proportion of susceptible individuals taking precautions, and the disease infection rate. Our results show that if the disease infection rate is less than 0.082/day, then R0 is always less than 1; and if at least 55.29% of the susceptible population take precautions such as regular hand washing with soap, use of sanitizers, and the wearing of face masks, then the reproduction number R0 remains below unity irrespective of the disease infection rate. Keeping R0 values below unity leads to a decrease in COVID-19 prevalence

Modelling adversarial dynamics in natural and artificial immunity

Immunity is both a lens to understand the ecology of adversarial host-pathogen interactions, but also a lever for clinical intervention in combating infectious disease. This thesis uses mathematical modelling to interrogate both the function and effectiveness of natural immune systems, and how human interventions like vaccination can be best deployed. A defence of the value of this scientific approach in overcoming the empirical and interpretative challenges for these topics is provided in chapter 1. The first two investigations consider the evolution and functional performance of natural immune systems. Chapter 2 proposes that immune adaptations can plausibly arise from Fisherian selection, and therefore could be maladaptive, and constructs a simple mathematical model of hosts and pathogens to examine this potential mechanism. Chapter 3 assesses the utility of a particular immune adaptation: fever. It models the impact of different proposed thermal strategies of fever in terms of suppressing pathogen temperature-dependent growth, and compares these to the calorimetric costs of heating. The second two investigations consider how artificial immunity is best deployed, focusing upon vaccination strategies in the COVID-19 pandemic. Chapter 4 considers the risk and benefit of very early emergency use of a vaccine, before its safety and efficacy is known, finding this balance can favour such use for many individuals in the early stages of the COVID-19 pandemic. Chapter 5 investigates another emergency strategy for multiple dose vaccines, prioritising individuals for first doses and the expense of postponing individuals receiving subsequent doses, and when this strategy would be beneficial for public health in terms of risk reduction, disease transmission, and earlier relaxation of non-pharmaceutical interventions. I conclude with a discussion of broader themes which span across these investigations, and suggestions for further research

Estudio del efecto de la vacunación en modelos de epidemias con transmisión estocástica

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Estudios Estadísticos, leída el 15-12-2022Mathematical epidemic models are frequently used in biology for analyzing transmission dynamics of infectious diseases and assessing control measures to interrupt their expansion. In order to select and develop properly the above mathematical models, it is necessary to take into account the particularities of an epidemic process as type of disease, mode of transmission and population characteristics. In this thesis we focus on infectious diseases with stochastic transmission including vaccination as a control measure to stop the spread of the pathogen. To that end, we consider constant and moderate size populations where individuals are homogeneously mixed. We assume that characteristics related to the transmission/recovery of the infectious disease present a common probabilistic behavior for individuals in the population. To assure herd immunity protection, we consider that a percentage of the population is protected against the disease by a vaccine, prior to the start of the outbreak.The administered vaccine is imperfect in the sense that some individuals, who have been previously vaccinated, failed to increase antibody levels and, in consequence, they could be infected. Pathogenic transmission occurs by direct contact with infected individuals. As population is not isolated, disease spreads from direct contacts with infected individuals inside or outside the population...Los modelos matemáticos epidemiológicos se usan frecuentemente en biología para analizar las dinámicas de transmisión de enfermedades infecciosas y para evaluar medidas de control con el objetivo de frenar su expansión. Para poder seleccionar y desarrollar adecuadamente estos modelos es necesario tener en cuenta las particularidades propias del proceso epidémico tales como el tipo de enfermedad, modo de transmisión y características de la población. En esta tesis nos centramos en el estudio de enfermedades de tipo infeccioso con transmisión por contacto directo, que disponen de una vacuna como medida de contención en la propagación del patógeno. Para ello, consideramos poblaciones de tamaño moderado, que permanece constante a lo largo de un brote y asumiremos que los individuos no tienen preferencia a la hora de relacionarse y que las características referentes a la transmisión de la enfermedad se representan en términos de variables aleatorias, comunes para todos los individuos. La población no está aislada y la transmisión del patógeno se produce mediante contacto directo con cualquier persona infectada, tanto de dentro de la población como fuera de ella. Asumimos que, antes del inicio del brote epidémico, se ha administrado la vacuna a un porcentaje suficiente de individuos de la población, de forma que se asegure la inmunidad de rebaño. Consideramos que la vacuna administrada es imperfecta en el sentido que algunos individuos vacunados no logran desarrollar anticuerpos frente a la enfermedad y por lo tanto, podrían resultar infectados al contactar con individuos enfermos...Fac. de Estudios EstadísticosTRUEunpu

Polyfunctional antibodies: a path towards precision vaccines for vulnerable populations

Vaccine efficacy determined within the controlled environment of a clinical trial is usually substantially greater than real-world vaccine effectiveness. Typically, this results from reduced protection of immunologically vulnerable populations, such as children, elderly individuals and people with chronic comorbidities. Consequently, these high-risk groups are frequently recommended tailored immunisation schedules to boost responses. In addition, diverse groups of healthy adults may also be variably protected by the same vaccine regimen. Current population-based vaccination strategies that consider basic clinical parameters offer a glimpse into what may be achievable if more nuanced aspects of the immune response are considered in vaccine design. To date, vaccine development has been largely empirical. However, next-generation approaches require more rational strategies. We foresee a generation of precision vaccines that consider the mechanistic basis of vaccine response variations associated with both immunogenetic and baseline health differences. Recent efforts have highlighted the importance of balanced and diverse extra-neutralising antibody functions for vaccine-induced protection. However, in immunologically vulnerable populations, significant modulation of polyfunctional antibody responses that mediate both neutralisation and effector functions has been observed. Here, we review the current understanding of key genetic and inflammatory modulators of antibody polyfunctionality that affect vaccination outcomes and consider how this knowledge may be harnessed to tailor vaccine design for improved public health

A multi-objective approach to estimate parameters of compartmental epidemiological models. Application to Ebola Virus Disease epidemics.

In this work, we propose a novel methodology to adjust parameters of compartmental epidemiological models. It is based on solving a multi-objective optimization problem that consists in fitting some of the model outputs to real observations. First, according to the available data of the considered epidemic, we define a multi-objective optimization problem where the model parameters are the optimization variables. Then, this problem is solved by considering a particular optimization algorithm called ParWASF-GA (ParallelWeighting Achievement Scalarizing Function Genetic Algorithm). Finally, the decision maker chooses, within the set of possible solutions, the values of parameters that better suit his/her preferences. In order to illustrate the benefit of using our approach, it is applied to estimate the parameters of a deterministic epidemiological model, called Be-CoDiS (Between-Countries Disease Spread), used to forecast the possible spread of human diseases within and between countries. We consider data from different Ebola outbreaks from 2014 up to 2019. In all cases, the proposed methodology helps to obtain reasonable predictions of the epidemic magnitudes with the considered model