Modeling population-wide testing of SARS-CoV-2 for containing COVID-19 pandemic in Okinawa, Japan

To break the chains of SARS-CoV-2 transmission and contain the coronavirus disease 2019 (COVID-19) pandemic, population-wide testing has been practiced in various countries. However, scant research has addressed this topic in Japan. In this modeling exercise, we extracted the number of daily reported cases of COVID-19 in Okinawa from October 1 to November 30, 2020, and explored possible scenarios for decreasing COVID-19 incidence by combining population-wide screening and/or social distancing policy. We reveal that permanent lockdown can be theoretically replaced by mass testing but sufficient target population at an adequate frequency must be mobilized. In addition, solely imposing a circuit breaker will not bring a favorable outcome in the long run, and mass testing presents implications for minimizing a period of lockdown. Our results highlight the importance of incentivizing citizens to join the frequent testing and ensure their appropriate isolation. This study also suggests that early containment of COVID-19 will be feasible in prefectures where the mobility is low and/or can be easily controlled for its geographic characteristics. Rigorous investment in public health will be manifestly vital to contain COVID-19

R0R_0 and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission

In this paper, we study an age-structured SIS epidemic model with periodicity and vertical transmission. We show that the spectral radius of the Frechet derivative of a nonlinear integral operator plays the role of a threshold value for the global behavior of the model, that is, if the value is less than unity, then the disease-free steady state of the model is globally asymptotically stable, while if the value is greater than unity, then the model has a unique globally asymptotically stable endemic (nontrivial) periodic solution. We also show that the value can coincide with the well-know epidemiological threshold value, the basic reproduction number $\mathcal{R}_0$

Hopf bifurcation in a chronological age-structured SIR epidemic model with age-dependent infectivity

In this paper, we examine the stability of an endemic equilibrium in a chronological age-structured SIR (susceptible, infectious, removed) epidemic model with age-dependent infectivity. Under the assumption that the transmission rate is a shifted exponential function, we perform a Hopf bifurcation analysis for the endemic equilibrium, which uniquely exists if the basic reproduction number is greater than $1$. We show that if the force of infection in the endemic equilibrium is equal to the removal rate, then there always exists a critical value such that a Hopf bifurcation occurs when the bifurcation parameter reaches the critical value. Moreover, even in the case where the force of infection in the endemic equilibrium is not equal to the removal rate, we show that if the distance between them is sufficiently small, then a similar Hopf bifurcation can occur. By numerical simulation, we confirm a special case where the stability switch of the endemic equilibrium occurs more than once

Global analysis of a multi-group SIR epidemic model with nonlinear incidence rates and distributed moving delays between patches

In this paper, applying Lyapunov functional approach, we establish sufficient conditions under which each equilibrium is globally asymptotically stable for a class of multi-group SIR epidemic models. The incidence rate is given by nonlinear incidence rates and distributed delays incorporating not only an exchange of individuals between patches through migration but also cross patch infection between different groups. We show that nonlinear incidence rates and distributed delays have no influence on the global stability, but patch structure has. Moreover, the present results generalize known results on the global stability of a heroin model with two delays considered in the recent literatures. We also offer new techniques to prove the boundedness of the solutions, the existence of the endemic equilibrium and permanence of the model

Hopf bifurcation in an age-structured SIR epidemic model

In this paper, we study the occurrence of a sustained periodic solution via the Hopf bifurcation in an age-structured SIR epidemic model. Under the assumption that the transmission rate depends on the age of infective individuals and the product of the transmission rate and the population age distribution is concentrated in a specific age, we reformulate the model into an integral equation of Fredholm type. We then define the basic reproduction number R-0 and show that the unique positive endemic equilibrium of the integral equation exists if and only if R0 > 1. We derive a characteristic equation for the endemic equilibrium, and regarding the specific age as a bifurcation parameter, we obtain a sufficient condition for the occurrence of the Hopf bifurcation. Finally, we provide a numerical example that supports our theoretical result

Prediction of the Epidemic Peak of Coronavirus Disease in Japan, 2020

The first case of coronavirus disease 2019 (COVID-19) in Japan was reported on 15 January 2020 and the number of reported cases has increased day by day. The purpose of this study is to give a prediction of the epidemic peak for COVID-19 in Japan by using the real-time data from 15 January to 29 February 2020. Taking into account the uncertainty due to the incomplete identification of infective population, we apply the well-known SEIR compartmental model for the prediction. By using a least-square-based method with Poisson noise, we estimate that the basic reproduction number for the epidemic in Japan is R0=2.6 ( 95% CI, 2.4 – 2.8 ) and the epidemic peak could possibly reach the early-middle summer. In addition, we obtain the following epidemiological insights: (1) the essential epidemic size is less likely to be affected by the rate of identification of the actual infective population; (2) the intervention has a positive effect on the delay of the epidemic peak; (3) intervention over a relatively long period is needed to effectively reduce the final epidemic size