Slow invariant manifold assessments in multi-route reaction mechanism

Optimal control problem arising from COVID-19 transmission model with rapid-test

The world health organization (WHO) has declared the Coronavirus (COVID-19) a pandemic. In light of this ongoing global issue, different health and safety measure has been recommended by the WHO to ensure the proactive, comprehensive, and coordinated steps to bring back the whole world into a normal situation. This is an infectious disease and can be modeled as a system of non-linear differential equations with reaction rates which consider the rapid-test as the intervention program. Therefore, we have developed the biologically feasible region, i.e., positively invariant for the model and boundedness solution of the system. Our system becomes well-posed mathematically and epidemiologically for sensitive analysis and our analytical result shows an occurrence of a forward bifurcation when the basic reproduction number is equal to unity. Further, the local sensitivities for each model state concerning the model parameters are computed using three different techniques: non-normalizations, half-normalizations, and full normalizations. The numerical approximations have been measured by using System Biology Toolbox (SBedit) with MATLAB, and the model is analyzed graphically. Our result on the sensitivity analysis shows a potential of rapid-test for the eradication program of COVID-19. Therefore, we continue our result by reconstructing our model as an optimal control problem. Our numerical simulation shows a time-dependent rapid test intervention succeeded in suppressing the spread of COVID-19 effectively with a low cost of the intervention. Finally, we forecast three COVID-19 incidence data from China, Italy, and Pakistan. Our result suggests that Italy already shows a decreasing trend of cases, while Pakistan is getting closer to the peak of COVID-19.

Dynamics models for identifying the key transmission parameters of the COVID-19 disease

After the analysis and forecast of COVID-19 spreading in China, Italy, and France the WHO has declared the COVID-19 a pandemic. There are around 100 research groups across the world trying to develop a vaccine for this coronavirus. Therefore, the quantitative and qualitative analysis of the COVID–19 pandemic is needed along with the effect of rapid test infection identification on controlling the spread of COVID-19. Mathematical models with computational simulations are the effective tools that help global efforts to estimate key transmission parameters and further improvements for controlling this disease. This is an infectious disease and can be modeled as a system of non-linear differential equations with reaction rates. In this paper, we develop the models for coronavirus disease at different stages with the addition of more parameters due to interactions among the individuals. Then, some key computational simulations and sensitivity analysis are investigated. Further, the local sensitivities for each model state concerning the model parameters are computed using the model reduction techniques: the dynamical models are eventually changed with the change of parameters are represented graphically.

A quantitative and qualitative analysis of the COVID-19 pandemic model

Global efforts around the world are focused on to discuss several health care strategies for minimizing the impact of the new coronavirus (COVID-19) on the community. As it is clear that this virus becomes a public health threat and spreading easily among individuals. Mathematical models with computational simulations are effective tools that help global efforts to estimate key transmission parameters and further improvements for controlling this disease. This is an infectious disease and can be modeled as a system of non-linear differential equations with reaction rates. This work reviews and develops some suggested models for the COVID-19 that can address important questions about global health care and suggest important notes. Then, we suggest an updated model that includes a system of differential equations with transmission parameters. Some key computational simulations and sensitivity analysis are investigated. Also, the local sensitivities for each model state concerning the model parameters are computed using three different techniques: non-normalizations, half normalizations, and full normalizations. Results based on the computational simulations show that the model dynamics are significantly changed for different key model parameters. Interestingly, we identify that transition rates between asymptomatic infected with both reported and unreported symptomatic infected individuals are very sensitive parameters concerning model variables in spreading this disease. This helps international efforts to reduce the number of infected individuals from the disease and to prevent the propagation of new coronavirus more widely on the community. Another novelty of this paper is the identification of the critical model parameters, which makes it easy to be used by biologists with less knowledge of mathematical modeling and also facilitates the improvement of the model for future development theoretically and practically.