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Since the beginning of March 2020, the cumulative numbers of cases of infection with the novel coronavirus SARS-CoV-2 in Germany have been reported on a daily basis. The reports originate from national laws, according to which positive test…

A primary quantity of interest in the study of infectious diseases is the average number of new infections that an infected person produces. This so-called reproduction number has significant implications for the disease progression. There…

COVID-19 pandemic has reshaped our world in a timescale much shorter than what we can understand. Particularities of SARS-CoV-2, such as its persistence in surfaces and the lack of a curative treatment or vaccine against COVID-19, have…

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible $S$, infected $I$, removed $R$ and dead people $D$. In order to have…

In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR)…

Although previous infection and vaccination provide protection against SARS-CoV-2 infection, both reinfection and breakthrough infection are possible events whose occurrence would increase with time after first exposure to the antigen and…

In December 2019, a newly discovered SARS-CoV-2 virus was emerged from China and propagated worldwide as a pandemic. In the absence of preventive medicine or a ready to use vaccine, mathematical models can provide useful scientific insights…

Predicting an accurate expected number of future COVID-19 cases is essential to properly evaluate the effectiveness of any treatment or preventive measure. This study aimed to identify the most appropriate mathematical model to…

In this paper, we present a model to predict the spread of the Covid-19 epidemic and apply it to the specific case of Italy. We started from a simple Susceptible, Infected, Recovered (SIR) model and we added the condition that, after a…

We develop a simple 3-dimensional iterative map model to forecast the global spread of the coronavirus disease. Our model contains at most two fitting parameters, which we determine from the data supplied by the world health organisation…

The COVID-19 pandemic has caused major disturbance to human life. An important reason behind the widespread social anxiety is the huge uncertainty about the pandemic. A fundamental uncertainty is how many or what percentage of people have…

Estimation of prevalence of undocumented SARS-CoV-2 infections is critical for understanding the overall impact of the Covid-19 disease. In fact, unveiling uncounted cases has fundamental implications for public policy interventions…

Different ways of calculating mortality ratios during epidemics have yielded very different results, particularly during the current COVID-19 pandemic. We formulate both a survival probability model and an associated infection…

In February 2020 the first human infection with SARS-CoV-2 was reported in Germany. Since then the local public health offices have been responsible to monitor and react to the dynamics of the pandemic. One of their major tasks is to…

We propose a simple model of spreading of some infection in an originally healthy population which is different from other models existing in the literature. In particular, we use an operator technique which allows us to describe in a…

A compartmental epidemic model is proposed to predict the Covid-19 virus spread. It considers: both detected and undetected infected populations, medical quarantine and social sequestration, release from sequestration, plus possible…

The outbreak of Coronavirus Disease 2019 (COVID-19) is an ongoing pandemic affecting over 200 countries and regions. Inference about the transmission dynamics of COVID-19 can provide important insights into the speed of disease spread and…

When the novel coronavirus disease SARS-CoV2 (COVID-19) was officially declared a pandemic by the WHO in March 2020, the scientific community had already braced up in the effort of making sense of the fast-growing wealth of data gathered by…

The COVID-19 pandemic has been a great catastrophe that upended human lives and caused millions of deaths all over the world. The rapid spread of the virus, with its early-stage exponential growth and subsequent 'waves', caught many medical…

We propose a deterministic SAIVRD model and a stochastic SARV model of the epidemic COVID-19 involving asymptomatic infections and vaccinations to conduct data forecasts using time-dependent parameters. The forecast by our deterministic…