Transmission analysis of COVID-19 with discrete time imported cases: Tianjin and Chongqing as cases

Abstract

In 2020, an unexpectedly large outbreak of the coronavirus disease 2019 (COVID-19) epidemic was reported in mainland China. As we known, the epidemic was caused by imported cases in other provinces of China except for Hubei in 2020. In this paper, we developed a differential equation model with tracing isolation strategy with close contacts of newly confirmed cases and discrete time imported cases, to perform assessment and risk analysis for COVID-19 outbreaks in Tianjin and Chongqing city. Firstly, the model behavior without imported cases was given. Then, the real-time regeneration number in Tianjin and Chongqing city revealed a trend of rapidly rising, and then falling fast. Finally, sensitivity analysis demonstrates that the earlier with Wuhan lock-down, the fewer cases in these two cities. One can obtain that the tracing isolation of close contacts of newly confirmed cases could effectively control the spread of the disease. But it is not sensitive for the more contact tracing isolation days on confirmed cases, the fewer cases. Our investigation model could be potentially helpful to provide model building technology for the transmission of COVID-19.

Inter-provincial disparity of COVID-19 transmission and control in Nepal

“…This pattern of the effective reproduction number identified with our approach is similar to the one computed using dynamical system model 33 . The maintenance of the effective reproduction number below 1 observed in our study due to the policies that control imported cases is consistent with the estimated low reproduction number in other places where inter-cities travel restrictions were imposed 36 , 39 , 41 . Despite a continuous flow of cases from India, one of the most COVID-19 affected countries in the world, the policies implemented by the Nepal government ideally controlled the local transmission, and thus deserve in-depth analysis to identify their local level impacts.…”

“…4 ). In line with our finding, the disparity in -trend has also been found in two cities of China where imported cases also contributed to the COVID-19 cases at the beginning of the epidemic 36 . Such wide disparities across provinces found by our study underscores that the analysis of country-level data might not be enough to implement policies for reducing province-level epidemic indicators.…”

“…In addition to the number and type of policies, the magnitude of effects of these policies is quite different from province to province (Table 4 ). In general, lockdown appeared to be the most effective policy to control most of the indicators, consistent with previous studies 33 , 36 , 37 , 39 , 40 , 42 , 43 , although there were some exceptions. Combining all these analyses, our results indicate that the net effect of the policies can be province-dependent despite the policy planning at national level, and thus province-level analysis is critical to proper implementation of government policies.…”

“…In Table 2 , we present the values of basic reproduction number along with their 95% confidence intervals for Nepal and its provinces. We estimated the basic reproduction number for the whole country to be 1.083 (95% CI 1.075–1.093 ) (Table 2 ), which is comparable to estimated for other countries 33 , 36 , 39 , 40 , 43 , 54 , 55 .…”

“…Some studies have provided estimates of the reproduction number using data from several places 14 , 35 – 38 and have observed its link to prevention strategies. Many variants of deterministic and stochastic models have also been developed 4 , 6 , 14 , 17 , 18 , 33 , 35 , 36 , 39 – 43 to predict COVID-19 transmission dynamics, estimate basic reproduction numbers, and examine intervention strategies such as travel ban, lockdown, isolation, and quarantine. While the previous studies have provided important insights into the on-going pandemic, none of these studies focused on epidemic indicators in the context of geographical (open-border) and population contact disparity that exists in places like the provinces of Nepal.…”