Mathematical modelling of COVID-19: a case study of Italy. (English) Zbl 1540.92008
Summary: This manuscript describes a mathematical epidemiological model of COVID-19 to investigate the dynamics of this pandemic disease and we have fitted this model to the current COVID-19 cases in Italy. We have obtained the basic reproduction number which plays a crucial role on the stability of disease free equilibrium point. Backward bifurcation with respect to the cure rate of treatment occurs conditionally. It is clear from the sensitivity analysis that the developments of self immunities with proper maintaining of social distancing of the exposed and asymptomatic individuals play key role for controlling the disease. We have validated the model by considering the COVID-19 cases of Italy and the future situations of epidemicity in Italy have been predicted from the model. We have estimated the basic reproduction number for the COVID-19 outbreak in Italy and effective reproduction number has also been studied. Finally, an optimal control model has been formulated and solved to realize the positive impacts of adapting lock down by many countries for maintaining social distancing.
MSC:
| 92-08 | Computational methods for problems pertaining to biology |
| 92D30 | Epidemiology |
| 37N25 | Dynamical systems in biology |
Keywords:
basic reproduction number; COVID-19; social distancing; lock down; incubation period; asymptomatic transmission; quarantine; backward bifurcation; effective reproduction number; optimal controlReferences:
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