A Study on COVID-19 Incidence in Europe through Two SEIR Epidemic Models Which Consider Mixed Contagions from Asymptomatic and Symptomatic Individuals

The impact of the SARS-CoV-2 (COVID-19) on the world has been partially controlled through different measures of social isolation and prophylaxis. Two new SEIR (Susceptible-Exposed-Infected-Recovered) models are proposed in order to describe this spread through different countries of Europe. In both models the infectivity of the asymptomatic period during the exposed stage of the disease will be taken into account. The different transmission rates of the SEIR models are calculated by considering the different locations and, more importantly, the lockdown measures implemented in each region. A new classification of these intervention measures will be set and their influence on the values of the transmission rates will be estimated through regression analysis.The authors are grateful to the institute Carlos III for grant COV20/01213, to the Spanish Government for Grants RTI2018-094336-B-I00 and RTI2018-094902-BC22 (MCIU/AEI/FEDER, UE) and to the Basque Government for Grant IT1207-19

A Modelization of the Propagation of COVID-19 in Regions of Spain and Italy with Evaluation of the Transmission Rates Related to the Intervention Measures

Two discrete mathematical SIR models (Susceptible-Infectious-Recovered) are proposed for modelling the propagation of the SARS-CoV-2 (COVID-19) through Spain and Italy. One of the proposed models is delay-free while the other one considers a delay in the propagation of the infection. The objective is to estimate the transmission, also known as infectivity rate, through time taking into account the infection evolution data supplied by the official health care systems in both countries. Such a parameter is estimated through time at different regional levels and it is seen to be strongly dependent on the intervention measures such as the total (except essential activities) or partial levels of lockdown. Typically, the infectivity rate evolves towards a minimum value under total lockdown and it increases again when the confinement measures are partially or totally removed.The authors are grateful to the institute Carlos III for grant COV20/01213, to the Spanish Government for Grants RTI2018- 094336-B-I00 and RTI2018-094902-B-C22 (MCIU/AEI/FEDER, UE) and to the Basque Government for Grant IT1207-19

Kontserbazio legeak dituzten deribatu partzialetako ekuazioetarako zenbakizko metodoak

[EUS] Lan honen helburua kontserbazio legeak dituzten deribatu partzialetako ekuazioak aztertu eta zenbakizko metodoak erabiliz ebaztea da. Graduan zehar ekuazio ez-linealak ez dira ia lantzen eta hortik dator motibazioa. Mota horretako ekuazioek zailtasun gehigarriak dituzte eta horiei aurre egiten ikasiko dugu. Lanaren hasieran kontserbazio legeen sarrera bat egingo da, segidan, Burgersen ekuazioa aurkeztuko da, lan guztian zehar kontserbazio legeen eredu izango dena, eta analitikoki ekuazioaren zenbait propietate garrantzitsu aztertuko dira. Ondoren, zenbakizko metodoen kontzeptu orokorren definizioak egingo dira eta zenbait zenbakizko eskema aurkeztuko dira Godunov-en metodoarekin bukatzeko. Lanaren amaieran, metodo horien zenbakizko simulazioak egingo dira bi problema zehatz ebazteko. Soluzioak eta grafikoak lortzeko Mathematica programa erabiliko da, grafikoak egin eta aztertzeko egokiena delako. Lan hau egiteko graduan zehar jasotako jakintzak praktikan jarriko dira: lehenik eta behin, zenbakizko metodoei buruzko hiru ikasgaietan ikasitako kontzeptuak (Zenbakizko metodoak I, Zenbakizko metodoak II eta Numerical solution of differential equation); bestetik, zenbait integral ulertzeko eta moldatzeko kalkulu diferentziala eta baita ekuazio diferentzialetan ikasitako teknikak ere; eta azkenik, zuzenean eragiten ez duten baina baliagarriak egingo diren hainbat jakintza, hala nola, neurria, programazioa, fisika orokorra edo kurbak eta geometria