scholarly journals Epidemic management with admissible and robust invariant sets

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257598
Author(s):  
Willem Esterhuizen ◽  
Jean Lévine ◽  
Stefan Streif

We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing, quarantining and vaccination. We describe the admissible and maximal robust positively invariant (MRPI) sets of these two models via the theory of barriers. We show how the sets may be used in the management of epidemics, for both perfect and imperfect/uncertain models, detailing how intervention strategies may be specified such that the hard infection cap is never breached, regardless of the basic reproduction number. The results are clarified with detailed examples.

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Brenda M. Samiadji ◽  
Gracia M. Simorangkir ◽  
Sarbaz H. A. Khosnaw ◽  
Muhammad Shahzad

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.


Author(s):  
Diego Chowell ◽  
Kimberlyn Roosa ◽  
Ranu Dhillon ◽  
Gerardo Chowell ◽  
Devabhaktuni Srikrishna

We investigate how individual protective behaviors, different levels of testing, and isolation influence the transmission and control of the COVID-19 pandemic. Based on an SEIR-type model incorporating asymptomatic but infectious individuals (40%), we show that the pandemic may be readily controllable through a combination of testing, treatment if necessary, and self-isolation after testing positive (TTI) of symptomatic individuals together with social protection (e.g., facemask use, handwashing). When the basic reproduction number, R0, is 2.4, 65% effective social protection alone (35% of the unprotected transmission) brings the R below 1. Alternatively, 20% effective social protection brings the reproduction number below 1.0 so long as 75% of the symptomatic population is covered by TTI within 12 hours of symptom onset. Even with 20% effective social protection, TTI of 1 in 4 symptomatic individuals can substantially 'flatten the curve' cutting the peak daily incidence in half.


2020 ◽  
Author(s):  
Hyojung Lee ◽  
Yeahwon Kim ◽  
Eunsu Kim ◽  
Sunmi ‍Lee

BACKGROUND The emergence of COVID-19 has posed a serious threat to humans all around the world despite recent achievements of vaccines, antiviral drugs, and medical infrastructure. Our modern society has evolved too complex and most of the countries are tightly connected on a global scale. This makes it nearly impossible to implement perfect and prompt mitigation strategies for the COVID-19 outbreaks. Especially, due to the explosive growth of international travels, the diverse network and complexity of human mobility become an essential factor that gives rise to the spread of COVID-19 globally within a very short time. OBJECTIVE South Korea is one of the countries that have experienced the early stage of the COVID-19 pandemic. In the absence of vaccines and treatments, South Korea has implemented and maintained stringent interventions such as large-scale epidemiological investigation, rapid diagnosis, social distancing, and prompt clinical classification of severe patients with appropriate medical measures. In particular, South Korea has been implementing effective screening and quarantine at the airport. In this work, we aim to investigate the impacts of such effective interventions on international travels which can prevent local transmission of COVID-19. METHODS The relation between the number of passengers and the number of imported cases were analyzed. Based on the relation, we have assessed the country-specific risk as the spread of COVID-19 gets expanded from January to October 2020. Moreover, a renewal mathematical modeling has been employed incorporating the risk assessment to capture both imported and local cases of COVID-19 in South Korea. We have estimated the basic reproduction number and the effective reproduction number accounting for both imported and local cases. RESULTS The basic reproduction number (R_0) was estimated at 1.87 (95% CI : 1.47, 2.35) with the rate (α =0.07)of the secondary transmission caused by the imported cases. The time-varying basic reproduction number (effective reproduction number, R_t) was estimated. Our results indicate that the prompt implementation of case-isolation and quarantine were effective to reduce the. secondary cases from imported cases in spite of constant inflows from high-risk countries of COVID-19 all throughout the year 2020. Moreover, various mitigation interventions including social distancing and movement restriction have been maintained effectively to reduce the spread of local cases in South Korea. CONCLUSIONS We have investigated the relative risk of importation of COVID-19, using the country-specific epidemiological data, and passenger volume. By combining the social distancing, screening, and self-quarantine for all travelers entering Korea, the mitigation of COVID-19 transmission caused by imported cases in Korea was highly successful. Those efforts, accompanied by identification of the source of infection, the strengthened quarantine measures for travelers from overseas countries, should be continued. However, the recent new coronavirus variant originated from South Africa has been threatening to get back to the strict border control and lockdown of all around the world again. Therefore, it is urgent to assess the importation risk and maintain an effective surveillance system of COVID-19 in South Korea.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Andrés Ríos-Gutiérrez ◽  
Soledad Torres ◽  
Viswanathan Arunachalam

AbstractIn this paper, we discuss the basic reproduction number of stochastic epidemic models with random perturbations. We define the basic reproduction number in epidemic models by using the integral of a function or survival function. We study the systems of stochastic differential equations for SIR, SIS, and SEIR models and their stability analysis. Some results on deterministic epidemic models are also obtained. We give the numerical conditions for which the disease-free equilibrium point is asymptotically stable.


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