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Background: The ongoing coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) and the Omicron variant presents a formidable challenge for control and prevention worldwide, especially for low- and middle-income countries (LMICs). Hence, taking Kazakhstan and Pakistan as examples, this study aims to explore COVID-19 transmission with the Omicron variant at different contact, quarantine and test rates. Methods: A disease dynamic model was applied, the population was segmented, and three time stages for Omicron transmission were established: the initial outbreak, a period of stabilization, and a second outbreak. The impact of population contact, quarantine and testing on the disease are analyzed in five scenarios to analysis their impacts on the disease. Four statistical metrics are employed to quantify the model's performance, including the correlation coefficient (CC), normalized absolute error, normalized root mean square error and distance between indices of simulation and observation (DISO). Results: Our model has high performance in simulating COVID-19 transmission in Kazakhstan and Pakistan with high CC values greater than 0.9 and DISO values less than 0.5. Compared with the present measures (baseline), decreasing (increasing) the contact rates or increasing (decreasing) the quarantined rates can reduce (increase) the peak values of daily new cases and forward (delay) the peak value times (decreasing 842 and forward 2 days for Kazakhstan). The impact of the test rates on the disease are weak. When the start time of stage II is 6 days, the daily new cases are more than 8 and 5 times the rate for Kazakhstan and Pakistan, respectively (29,573 vs. 3259; 7398 vs. 1108). The impact of the start times of stage III on the disease are contradictory to those of stage II. Conclusions: For the two LMICs, Kazakhstan and Pakistan, stronger control and prevention measures can be more effective in combating COVID-19. Therefore, to reduce Omicron transmission, strict management of population movement should be employed. Moreover, the timely application of these strategies also plays a key role in disease control. [ABSTRACT FROM AUTHOR]

Taylor diagram has been frequently used to evaluate climate or hydrology models or data. A Taylor diagram summarizes three frequently used metrics including correlation coefficient (CC), standard deviation (STD), and centred root mean square error (RMSEc). Although these three metrics are relevant metrics for some applications, in some cases, additional indicators are needed, which calls for a new method. This study firstly addressed the short comments about the distance between indices of simulation and observation (DISO) described in a previous study. Secondly, the number of statistical metrics of DISO is extended from 3 to more than 3. The statistical metrics of the expanded DISO are more flexible than the Taylor diagram which uses the three fixed metrics. Thirdly, the current work compares the Taylor diagram with the expanded DISO in terms of their theoretical bases, revealing the advantage of DISO in terms of its flexibility in the selection of different types of metrics, and its suitability as an effective single metric to express a model's or dataset's overall quality. The power and flexibility of the expanded DISO are discussed. [ABSTRACT FROM AUTHOR]

Climate models use quantitative methods to simulate the interactions of the important drivers of climate system, to reveal the corresponding physical mechanisms, and to project the future climate dynamics among atmosphere, oceans, land surface and ice, such as regional climate models and global climate models. A comprehensive assessment of these climate models is important to identify their different overall performances, such as the accuracy of the simulated temperature and precipitation against the observed field. However, until now, the comprehensive performances of these models have not been quantified by a comprehensive index except the existed single statistical index, such as correlation coefficient (r), absolute error (AE), and the root‐mean‐square error (RMSE). To address this issue, therefore, in this study, a new comprehensive index Distance between Indices of Simulation and Observation (DISO) is developed to describe the overall performances of different models against the observed field quantitatively. This new index DISO is a merge of different statistical metrics including r, AE, and RMSE according to the distance between the simulated model and observed field in a three‐dimension space coordinate system. From the relationship between AE, RMSE, and RMS difference (RMSD) (i.e., standard deviation [SD] of bias time series), the new index also has the information of RMSD which is the statistical index in Taylor diagram. An example is applied objectively to display the applications of DISO and Taylor diagram in identifying the overall performances of different simulated models. Overall, with the strong physical characteristic of the distance in three dimensional space and the strict mathematical proof, the new comprehensive index DISO can convey the performances among different models. It can be applied in the comparison between different model data and in tracking changes in their performances. [ABSTRACT FROM AUTHOR]

Discrete epidemic models are popularly used to detect the pathogenesis, spreading, and controlling of the diseases. The three-dimensional discrete ${SIRS}$ epidemic models are more suitable than the two-dimensional discrete models to describe the spreading characters of the diseases. In this paper, the complex dynamical behaviors of a three-dimensional discrete ${SIRS}$ epidemic model with standard incidence rate are discussed. We choose the time step size parameter as a bifurcation parameter, the existence, stability, and direction of Hopf bifurcation are proved by using the normal form theorem and bifurcation theory. Moreover, the numerical simulations not only illustrate our results, but they also exhibit the complex dynamical behaviors, such as the invariant cycle, period-7 orbits and period-12 orbits with more than one attractors and chaotic sets. The flip bifurcation caused by the step size parameter is also obtained by a numerical simulation. Most importantly, when the adequate contact rate and the death rate of the infective individuals are chosen as the bifurcation parameters, there also exist a Hopf bifurcation, a flip bifurcation, chaos, and strange attractors. These results provide significant information for the disease controlling when there appear complex dynamical behaviors in the epidemic model. [ABSTRACT FROM AUTHOR]