How efficient is contact tracing in mitigating the spread of COVID-19? a mathematical modeling approach.

Contact Tracing (CT) is one of the measures taken by government and health officials to reduce the spread of the novel coronavirus. In this paper, we investigate its efficacy by developing a compartmental model for assessing its impact on mitigating the spread of the virus. We describe the impact on the reproduction number R 0 of COVID-19. In particular, we discuss the importance and relevance of parameters of the model such as the number of reported cases, effectiveness of tracking and monitoring policy, and the transmission rates to contact tracing. We describe the terms "perfect tracking", "perfect monitoring" and "perfect reporting" to indicate that traced contacts will be tracked while incubating, tracked contacts are efficiently monitored so that they do not cause secondary infections, and all infected persons are reported, respectively. We consider three special scenarios: (1) perfect monitoring and perfect tracking of contacts of a reported case, (2) perfect reporting of cases and perfect monitoring of tracked reported cases and (3) perfect reporting and perfect tracking of contacts of reported cases. Furthermore, we gave a lower bound on the proportion of contacts to be traced to ensure that the effective reproduction, R c , is below one and describe R c in terms of observable quantities such as the proportion of reported and traced cases. Model simulations using the COVID-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of COVID-19 and reduce peak hospitalizations and deaths. In particular, our findings suggest that effective monitoring policy of tracked cases and tracking of traced contacts while incubating are more crucial than tracing more contacts. The use of CT coupled with other measures such as social distancing, use of face mask, self-isolation or quarantine and lockdowns will greatly reduce the spread of the epidemic as well as peak hospitalizations and total deaths.

A fractional-order compartmental model for the spread of the COVID-19 pandemic.

We propose a time-fractional compartmental model (SEI A I S HRD) comprising of the susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized, recovered and dead population for the COVID-19 pandemic. We study the properties and dynamics of the proposed model. The conditions under which the disease-free and endemic equilibrium points are asymptotically stable are discussed. Furthermore, we study the sensitivity of the parameters and use the data from Tennessee state (as a case study) to discuss identifiability of the parameters of the model. The non-negative parameters in the model are obtained by solving inverse problems with empirical data from California, Florida, Georgia, Maryland, Tennessee, Texas, Washington and Wisconsin. The basic reproduction number is seen to be slightly above the critical value of one suggesting that stricter measures such as the use of face-masks, social distancing, contact tracing, and even longer stay-at-home orders need to be enforced in order to mitigate the spread of the virus. As stay-at-home orders are rescinded in some of these states, we see that the number of cases began to increase almost immediately and may continue to rise until the end of the year 2020 unless stricter measures are taken.

Fractional model for the spread of COVID-19 subject to government intervention and public perception.

COVID-19 pandemic has impacted people all across the world. As a result, there has been a collective effort to monitor, predict, and control the spread of this disease. Among this effort is the development of mathematical models that could capture accurately the available data and simulate closely the futuristic scenarios. In this paper, a fractional-order memory-dependent model for simulating the spread of COVID-19 is proposed. In this model, the impact of governmental interventions and public perception are incorporated as part of the nonlinear time-varying transmission rate. In addition, an algorithm for approximating the optimal values of the fractional order and strength of governmental interventions is provided. This approach makes our model suitable for capturing the given data set and consequently reliable for future predictions. The model simulation is performed using the two-step generalized exponential time-differencing method and tested for data from Mainland China, Italy, Saudi Arabia and Brazil. The simulation results demonstrate that the fractional order model calibrates to the data better than its integer order counterpart. This observation is further endorsed by the calculated error metrics.

Data-Driven Deep-Learning Algorithm for Asymptomatic COVID-19 Model with Varying Mitigation Measures and Transmission Rate.

Epidemiological models with constant parameters may not capture satisfactory infection patterns in the presence of pharmaceutical and non-pharmaceutical mitigation measures during a pandemic, since infectiousness is a function of time. In this paper, an Epidemiology-Informed Neural Network algorithm is introduced to learn the time-varying transmission rate for the COVID-19 pandemic in the presence of various mitigation scenarios. There are asymptomatic infectives, mostly unreported, and the proposed algorithm learns the proportion of the total infective individuals that are asymptomatic infectives. Using cumulative and daily reported cases of the symptomatic infectives, we simulate the impact of non-pharmaceutical mitigation measures such as early detection of infectives, contact tracing, and social distancing on the basic reproduction number. We demonstrate the effectiveness of vaccination on the transmission of COVID-19. The accuracy of the proposed algorithm is demonstrated using error metrics in the data-driven simulation for COVID-19 data of Italy, South Korea, the United Kingdom, and the United States.