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Diagnostic testing followed by isolation of identified cases with subsequent tracing and quarantine of close contacts—often referred to as test-trace-isolate-and-quarantine (TTIQ) strategy—is one of the cornerstone measures of infectious disease control. The COVID-19 pandemic has highlighted that an appropriate response to outbreaks of infectious diseases requires a firm understanding of the effectiveness of such containment strategies. To this end, mathematical models provide a promising tool. In this work, we present a delay differential equation model of TTIQ interventions for infectious disease control. Our model incorporates the assumption of limited TTIQ capacities, providing insights into the reduced effectiveness of testing and tracing in high prevalence scenarios. In addition, we account for potential transmission during the early phase of an infection, including presymptomatic transmission, which may be particularly adverse to a TTIQ based control. Our numerical experiments inspired by the early spread of COVID-19 in Germany demonstrate the effectiveness of TTIQ in a scenario where immunity within the population is low and pharmaceutical interventions are absent, which is representative of a typical situation during the (re-)emergence of infectious diseases for which therapeutic drugs or vaccines are not yet available. Stability and sensitivity analyses reveal both disease-dependent and disease-independent factors that impede or enhance the success of TTIQ. Studying the diminishing impact of TTIQ along simulations of an epidemic wave, we highlight consequences for intervention strategies. [ABSTRACT FROM AUTHOR]

SEIR (Susceptible–Exposed–Infected–Recovered) approach is a classic modeling method that is frequently used to study infectious diseases. However, in the vast majority of such models transitions from one population group to another are described using the mass-action law. That causes inability to reproduce observable dynamics of an infection such as the incubation period or progression of the disease's symptoms. In this paper, we propose a new approach to simulate the epidemic dynamics based on a system of differential equations with time delays and instant transitions to approximate durations of transition processes more correctly and make model parameters more clear. The suggested approach can be applied not only to Covid-19 but also to the study of other infectious diseases. We utilized it in the development of the delay-based model of the COVID-19 pandemic in Germany and France. The model takes into account testing of different population groups, symptoms progression from mild to critical, vaccination, duration of protective immunity and new virus strains. The stringency index was used as a generalized characteristic of the non-pharmaceutical government interventions in corresponding countries to contain the virus spread. The parameter identifiability analysis demonstrated that the presented modeling approach enables to significantly reduce the number of parameters and make them more identifiable. Both models are publicly available. [ABSTRACT FROM AUTHOR]

This work aims to assess the impact of renewable energy incentives, particularly that of the feed-in tariff (FiT), on the long-term development of solar photovoltaics (PVs). With this aim, the paper introduces a dynamic model based on nonlinear delay differential algebraic equations to simulate the evolution of the PV capacity and its commitment in the power grid. The model assumes the FiT budget, the PV cost and willingness of the public to install PVs as the main drivers for solar PV installations. In particular, the learning-by-doing concept to model the PV cost and consequently the PV deployment is proposed for the first time in this paper. The accuracy of the model is validated against historical data of two of the biggest PV markets in the world driven by FiT, namely, Italy during 2008–2014, and Germany during 2000–2014. A sensitivity analysis based on the Italian PV market is carried out to identify the impact of the parameters of the proposed model. Results indicate that the proposed model is a valuable tool that can help policymakers in the decision-making process, such as the definition of the FiT price and the duration of the incentives. [ABSTRACT FROM AUTHOR]