Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method

In this study, numerical treatment of liquid crystal model described through Hunter-Saxton equation (HSE) has been presented by sinc collocation technique through theta weighted scheme due to its enormous applications including, defects, phase diagrams, self-assembly, rheology, phase transitions, interfaces, and integrated biological applications in mesophase materials and processes. Sinc functions provide the procedure for function approximation over all types of domains containing singularities, semi-infinite or infinite domains. Sinc functions have been used to reduce HSE into an algebraic system of equations that makes the solution quite superficial. These algebraic equations have been interpreted as matrices. This projected that sinc collocation technique is considerably efficacious on computational ground for higher accuracy and convergence of numerical solutions. Stability analysis of the proposed technique has ensured the accuracy and reliability of the method, moreover, as the stability parameter satisfied the condition the proposed solution of the problem converges. The solution of the HSE is presented through graphical figures and tables for different cases that are constructed on various values of θ and collocation points. The accuracy and efficiency of the proposed technique is analyzed on the basis of absolute errors.This research has been partially supported by Ministerio de Ciencia, Innovación y Universidades grant number PGC2018-0971-B-100 and Fundación Séneca -Agencia de Ciencia y Tecnología de la Región de Murcia grant number 20783/PI/18. Also, It has been supported by the National Research Program for Universities (NRPU), Higher Education Commission, Pakistan, No. 8103/Punjab/NRPU/R and D/HEC/2017

Critical fluctuations in epidemic models explain COVID-19 post-lockdown dynamics

As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves, even when the community disease transmission rate β is not significantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, β> βc) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, β< βc) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with r(t) ≈ 1 hovering around its threshold value.Fil: Aguiar, Maíra. Basque Center for Applied Mathematics; España. Ikerbasque; España. Universita degli Studi di Trento; ItaliaFil: Van Dierdonck, Joseba Bidaurrazaga. Basque Health Department; EspañaFil: Mar, Javier. Debagoiena Integrated Healthcare Organisation; España. Biodonostia Health Research Institute; España. Kronikgune Institute for Health Services Research; EspañaFil: Cusimano, Nicole. Basque Center for Applied Mathematics; EspañaFil: Knopoff, Damián Alejandro. Basque Center for Applied Mathematics; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Anam, Vizda. Basque Center for Applied Mathematics; EspañaFil: Stollenwerk, Nico. Basque Center for Applied Mathematics; España. Universita degli Studi di Trento; Itali

Mathematical models for dengue fever epidemiology: A 10-year systematic review

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in

Prescriptive, descriptive or predictive models: What approach should be taken when empirical data is limited? Reply to comments on “Mathematical models for Dengue fever epidemiology: A 10-year systematic review”

1. BERC 2022-2025 program 2. Ministry of Sciences, Innovation and Universi- ties: BCAM Severo Ochoa accreditation CEX2021-001142-S / MICIN / AEI / 10.13039/501100011033 3. M.A. has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska- Curie grant agreement No 792494