Highlights Mathematical considerations of a SEIQR model to describe the propagation of COVID-19 are proposed. We derive analytically the reproductive number and the equilibria with and without COVID-19. Necessary and sufficient conditions for the stability of the equilibria are mathematically established. An efficient nonstandard method to solve the continuous problem is proposed and analyzed. The numerical simulations confirm the analytical and numerical results derived in this work.

In this manuscript, the mathematical analysis of corona virus model with time delay effect is studied. Mathematical modelling of infectious diseases has substantial role in the different disciplines such as biological, engineering, physical, social, behavioural problems and many more. Most of infectious diseases are dreadful such as HIV/AIDS, Hepatitis and 2019-nCov. Unfortunately, due to the non-availability of vaccine for 2019-nCov around the world, the delay factors like, social distancing, quarantine, travel restrictions, holidays extension, hospitalization and isolation are used as key tools to control the pandemic of 2019-nCov. We have analysed the reproduction number 𝐑𝐑 𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧 of delayed model. Two key strategies from the reproduction number of 2019-nCov model, may be followed, according to the nature of the disease as if it is diminished or present in the community. The more delaying tactics eventually, led to the control of pandemic. Local and global stability of 2019-nCov model is presented for the strategies. We have also investigated the effect of delay factor on reproduction number 𝐑𝐑 𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧 . Finally, some very useful numerical results are presented to support the theoretical analysis of the model.

In the present study, a nonlinear delayed coronavirus pandemic model is investigated in the human population. For study, we find the equilibria of susceptible-exposed-infected-quarantine-recovered model with delay term. The stability of the model is investigated using well-posedness, Routh Hurwitz criterion, Volterra Lyapunov function, and Lasalle invariance principle. The effect of the reproduction number on dynamics of disease is analyzed. If the reproduction number is less than one then the disease has been controlled. On the other hand, if the reproduction number is greater than one then the disease has become endemic in the population. The effect of the quarantine component on the reproduction number is also investigated. In the delayed analysis of the model, we investigated that transmission dynamics of the disease is dependent on delay terms which is also reflected in basic reproduction number. At the end, to depict the strength of the theoretical analysis of the model, computer simulations are presented.

This article represents a numerical analysis for a stochastic dengue epidemic model with incubation period of virus. We discuss the comparison of solutions between the stochastic dengue model and a deterministic dengue model. In this paper, we have shown that the stochastic dengue epidemic model is more realistic as compared to the deterministic dengue epidemic model. The effect of threshold number R 1 holds in the stochastic dengue epidemic model. If R 1 < 1, then situation helps us to control the disease while R 1 > 1 shows the persistence of disease in population. Unfortunately, the numerical methods like Euler-Maruyama, stochastic Euler, and stochastic Runge-Kutta do not work for large time step sizes. The proposed framework of stochastic nonstandard finite difference scheme (SNSFD) is independent of step size and preserves all the dynamical properties like positivity, boundedness, and dynamical consistency.

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