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Highlights A new mathematical model on COVID-19 that incorporates imperfect lockdown effect. Backward bifurcation occurs in COVID-19 transmission dynamics cause by imperfect nature of the lockdown efficacy. Under which backward bifurcation does not occur have been identified. Several model parameters as well as the basic reproduction number are estimated. The epidemic trend of COVID-19 in India, Mexico, South Africa and Argentina are predicted by our proposed model.

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An outbreak of the COVID-19 pandemic is a major public health disease as well as a challenging task to people with comorbidity worldwide. According to a report, comorbidity enhances the risk factors with complications of COVID-19. Here, we propose and explore a mathematical framework to study the transmission dynamics of COVID-19 with comorbidity. Within this framework, the model is calibrated by using new daily confirmed COVID-19 cases in India. The qualitative properties of the model and the stability of feasible equilibrium are studied. The model experiences the scenario of backward bifurcation by parameter regime accounting for progress in susceptibility to acquire infection by comorbidity individuals. The endemic equilibrium is asymptotically stable if recruitment of comorbidity becomes higher without acquiring the infection. Moreover, a larger backward bifurcation regime indicates the possibility of more infection in susceptible individuals. A dynamics in the mean fluctuation of the force of infection is investigated with different parameter regimes. A significant correlation is established between the force of infection and corresponding Shannon entropy under the same parameters, which provides evidence that infection reaches a significant proportion of the susceptible.

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