An outbreak of rapidly spreading coronavirus established human to human transmission and now became a pandemic across the world. The new confirmed cases of infected individuals of COVID-19 are increasing day by day. Therefore, the prediction of infected individuals has become of utmost important for health care arrangements and to control the spread of COVID-19. In this study, we propose a compartmental epidemic model with intervention strategies such as lockdown, quarantine, and hospitalization. We compute the basic reproduction number (R₀), which plays a vital role in mathematical epidemiology. Based on R₀, it is revealed that the system has two equilibrium, namely disease-free and endemic. We also demonstrate the non-negativity and boundedness of the solutions, local and global stability of equilibria, transcritical bifurcation to analyze its epidemiological relevance. Furthermore, to validate our system, we fit the cumulative and new daily cases in India. We estimate the model parameters and predict the near future scenario of the disease. The global sensitivity analysis has also been performed to observe the impact of different parameters on R₀. We also investigate the dynamics of disease in respect of different situations of lockdown, e.g., complete lockdown, partial lockdown, and no lockdown. Our analysis concludes that if there is partial or no lockdown case, then endemic level would be high. Along with this, the high transmission rate ensures higher level of endemicity. From the short time prediction, we predict that India may face a crucial phase (approx 6000000 infected individuals within 140 days) in near future due to COVID-19. Finally, numerical results show that COVID-19 may be controllable by reducing the contacts and increasing the efficacy of lockdown.

中文翻译：

---

COVID-19传播的数学模型：干预策略和锁定的作用

迅速传播的冠状病毒爆发建立了人与人之间的传播，现在已成为全世界的大流行病。新确诊的受感染的COVID-19个体的病例正在逐日增加。因此，对受感染个体的预测对于医疗保健安排和控制COVID-19的传播已变得至关重要。在这项研究中，我们提出了一种隔间流行病模型，该模型具有诸如锁定，隔离和住院等干预策略。我们计算了基本繁殖数（R ₀），它在数学流行病学中起着至关重要的作用。基于R ₀，表明该系统具有两个平衡，即无病性和地方性。我们还证明了解决方案的非负性和有界性，均衡的局部和全局稳定性，跨临界分叉以分析其流行病学相关性。此外，为了验证我们的系统，我们适合印度的累积和每日新病例。我们估计模型参数并预测疾病的近期发展。还进行了全局灵敏度分析，以观察不同参数对R _0的影响。我们还针对锁定的不同情况（例如完全锁定，部分锁定和无锁定）调查了疾病的动态。我们的分析得出的结论是，如果没有部分或没有锁定案例，则流行水平会很高。随之而来的是，高传输速率确保了更高的流行性。从短期预测中，我们预测，由于COVID-19，印度可能在不久的将来面临一个关键阶段（140天内大约600万受感染的人）。最后，数值结果表明，COVID-19可以通过减少接触并提高锁定效率来控制。