We propose a new mathematical model to investigate the recent outbreak of the coronavirus disease (COVID-19). The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents an epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. The global asymptotic stability conditions for the disease free equilibrium are obtained. The real COVID-19 incidence data entries from 01 July, 2020 to 14 August, 2020 in the country of Pakistan are used for parameter estimation thereby getting fitted values for the biological parameters. Sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. To view more features of the state variables in the proposed model, we perform numerical simulations by using different values of some essential parameters. Moreover, profiles of the reproduction number through contour plots have been biologically explained.

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ABSTRACT:In this paper, a deterministic mathematical model is formulated to analyse the degree of sensitivity of some factors that aid cholera transmission and management. We obtain the disease-free equilibrium point and conduct the local stability of the disease-free and endemic equilibria of the model. Reproduction number with interventions is stated and the method of normalised forward sensitivity index is employed to determine the numerical value of the key model parameters with respect to the effective reproduction number in order to determine their relative importance to cholera transmission and management. The results obtained show that the most important parameter to cholera transmission is the contact rate between susceptible and infectious individuals while the most crucial parameter to cholera management is the rate of cholera awareness.

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