Analysis of SIQR type mathematical model under Atangana-Baleanu fractional differential operator.

In the given manuscript, the fractional mathematical model for the current pandemic of COVID-19 is investigated. The model is composed of four agents of susceptible (S), infectious (I), quarantined (Q) and recovered (R) cases respectively. The fractional operator of Atangana-Baleanu-Caputo (ABC) is applied to the considered model for the fractional dynamics. The basic reproduction number is computed for the stability analysis. The techniques of existence and uniqueness of the solution are established with the help of fixed point theory. The concept of stability is also derived using the Ulam-Hyers stability technique. With the help of the fractional order numerical method of Adams-Bashforth, we find the approximate solution of the said model. The obtained scheme is simulated on different fractional orders along with the comparison of integer orders. Varying the numerical values for the contact rate ζ, different simulations are performed to check the effect of it on the dynamics of COVID-19.

Modeling the transmission dynamics of middle eastern respiratory syndrome coronavirus with the impact of media coverage.

Middle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R 0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.

Modeling the pandemic trend of 2019 Coronavirus with optimal control analysis.

In this work, we propose a mathematical model to analyze the outbreak of the Coronavirus disease (COVID-19). The proposed model portrays the multiple transmission pathways in the infection dynamics and stresses the role of the environmental reservoir in the transmission of the disease. The basic reproduction number R 0 is calculated from the model to assess the transmissibility of the COVID-19. We discuss sensitivity analysis to clarify the importance of epidemic parameters. The stability theory is used to discuss the local as well as the global properties of the proposed model. The problem is formulated as an optimal control one to minimize the number of infected people and keep the intervention cost as low as possible. Medical mask, isolation, treatment, detergent spray will be involved in the model as time dependent control variables. Finally, we present and discuss results by using numerical simulations.