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Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic…
Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with…
Without vaccines and treatments, societies must rely on non-pharmaceutical intervention strategies to control the spread of emerging diseases such as COVID-19. Though complete lockdown is epidemiologically effective, because it eliminates…
We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number $\mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters with a…
Measuring the prevalence of active SARS-CoV-2 infections in the general population is difficult because tests are conducted on a small and non-random segment of the population. However, people admitted to the hospital for non-COVID reasons…
The SIR pandemic model suffers from an unrealistic assumption: The rate of removal from the infectious class of individuals is assumed to be proportional to the number of infectious individuals. This means that a change in the rate of…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
Contacts between people are the absolute drivers of contagious respiratory infections. For this reason, limiting and tracking contacts is a key strategy for the control of the COVID-19 epidemic. Digital contact tracing has been proposed as…
In this paper, we present a discrete-time networked SEIR model using population flow, its derivation, and assumptions under which this model is well defined. We identify properties of the system's equilibria, namely the healthy states. We…
The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures.…
During the COVID-19 pandemic, many institutions such as universities and workplaces implemented testing regimens with every member of some population tested longitudinally, and those testing positive isolated for some time. Although the…
We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The…
This contribution analyzes the COVID-19 outbreak by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. This is done by an algorithm…
To control the current outbreak of the Coronavirus Disease 2019, constant monitoring of the epidemic is required since, as of today, no vaccines or antiviral drugs against it are known. We provide daily updated estimates of the reproduction…
Current efforts of modelling COVID-19 are often based on the standard compartmental models such as SEIR and their variations. As pre-symptomatic and asymptomatic cases can spread the disease between populations through travel, it is…
We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than…
The recent COVID-19 pandemic highlighted the need of non-pharmaceutical interventions in the first stages of a pandemic. Among these, lockdown policies proved unavoidable yet extremely costly from an economic perspective. To better…
A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…
There are many sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely…
This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total…