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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]