Mathematical modeling plays an important role to better understand the disease dynamics and designing strategies to manage quickly spreading infectious diseases in lack of an effective vaccine or specific antivirals. During this period, forecasting is of utmost priority for health care planning and to combat COVID-19 pandemic. In this study, we proposed and extended classical SEIR compartment model refined by contact tracing and hospitalization strategies to explain the COVID-19 outbreak. We calibrated our model with daily COVID-19 data for the five provinces of India namely, Kerala, Karnataka, Andhra Pradesh, Maharashtra, West Bengal and the overall India. To identify the most effective parameters we conduct a sensitivity analysis by using the partial rank correlation coefficients techniques. The value of those sensitive parameters were estimated from the observed data by least square method. We performed sensitivity analysis for $R_0$ to investigate the relative importance of the system parameters. Also, we computed the sensitivity indices for $R_0$ to determine the robustness of the model predictions to parameter values. Our study demonstrates that a critically important strategy can be achieved by reducing the disease transmission coefficient ${\beta }_s$ and clinical outbreak rate $q_a$ to control the COVID-19 outbreaks. Performed short-term predictions for the daily and cumulative confirmed cases of COVID-19 outbreak for all the five provinces of India and the overall India exhibited the steady exponential growth of some states and other states showing decays of daily new cases. Long-term predictions for the Republic of India reveals that the COVID-19 cases will exhibit oscillatory dynamics. Our research thus leaves the option open that COVID-19 might become a seasonal disease. Our model simulation demonstrates that the COVID-19 cases across India at the end of September 2020 obey a power law.

数学模型对于更好地了解疾病动态和设计在缺乏有效疫苗或特定抗病毒药物的情况下管理快速传播的传染病的策略发挥着重要作用。在此期间，预测对于医疗保健规划和抗击 COVID-19 大流行至关重要。在本研究中，我们提出并扩展了通过接触者追踪和住院策略改进的经典 SEIR 隔室模型，以解释 COVID-19 的爆发。我们使用印度五个省（喀拉拉邦、卡纳塔克邦、安得拉邦、马哈拉施特拉邦、西孟加拉邦和整个印度）的每日 COVID-19 数据校准了我们的模型。为了确定最有效的参数，我们使用偏秩相关系数技术进行敏感性分析。这些敏感参数的值是通过最小二乘法根据观测数据估计的。我们进行了敏感性分析${右}_0$研究系统参数的相对重要性。此外，我们还计算了敏感度指数${右}_0$确定模型预测对参数值的鲁棒性。我们的研究表明，通过降低疾病传播系数可以实现至关重要的策略${\beta }_s$和临床爆发率$q_A$以控制 COVID-19 的爆发。对印度所有五个省份的每日和累计确诊病例数和累计确诊病例数进行了短期预测，印度整体表现出一些邦的稳定指数增长，而其他邦的每日新增病例数则呈下降趋势。对印度共和国的长期预测表明，COVID-19 病例将呈现振荡动态。因此，我们的研究为 COVID-19 可能成为一种季节性疾病留下了可能性。我们的模型模拟表明，2020 年 9 月底印度各地的 COVID-19 病例遵循幂律。