COVID-19 Model Based on Conformable Fractional Derivativeand Its Numerical Solution

After the outbreak of COVID-19, it is of great significance to find an appropriate dynamic model of COVID-19 epidemic in order to master its transmission law, predict its development trend, and provide corresponding prevention and control basis. In this paper, the SEIRV chamber model is adopted, and the dynamics model of infectious disease is established by combining the fractional derivative of Conformable. The fractional derivative differential equation of Conformable is discretized by numerical method and its numerical solution is obtained. In addition, numerical simulation was carried out on the confirmed data of Wuhan city from January 23, 2020 to February 11, 2020. At the same time, consider that the Wuhan municipal government revised the epidemic data on February 12, 2020, adding nearly 14,000 people. The order α value of SEIRV model is modified, and then the revised data is simulated. The simulation results are in good agreement with the published data. The results show that compared with the traditional integer order model, the fractional order model can simulate the modified data. This reflects the advantages of fractional infectious disease dynamics model, and can provide certain reference value for the prediction of COVID-19 model. © 2022 Editorial Borad of Complex Systems and Complexity Science. All rights reserved.

International trade resilience with applied welfare economics: an analysis on personal protective equipment

A global crisis such as a pandemic causes a decrease in the global trade of medical supplies. One of the most significant issues healthcare workers and people face is the shortage of personal protective equipment (PPE) items. This study constructs the first international trade model to link infectious disease dynamics and global trade networks, considering the important relationship between government preparedness, domestic manufacturers, and consumers. We examine social welfare measures here in the presence of quantity controls and taxes on the global trade flows. An equilibrium coverage among countries is investigated that integrates net government revenue, purchasing cost, transportation cost, and the health cost caused by the shortage of PPE supply. We develop an optimisation model that balances domestic firms and the global trade network to satisfy the total demand for each traded PPE product. The proportional change in value-added on domestic production is also studied by considering the marginal manufacturing costs of a face mask. The results obtained from testing our model show that the average quantity coverage by the global trade networks among four countries decreased by up to 28 % using the proposed trade policy. Hence, a large amount of demand is met by relying on domestic production.

Nonlinear time-series forecasts for decision support: short-term demand for ICU beds in Santiago, Chile, during the 2021 COVID-19 pandemic.

In Chile, due to the explosive increase of new Coronavirus disease 2019 (COVID-19) cases during the first part of 2021, the ability of health services to accommodate new incoming cases was jeopardized. It has become necessary to be able to manage intensive care unit (ICU) capacity, and for this purpose, monitoring both the evolution of new cases and the demand for ICU beds has become urgent. This paper presents short-term forecast models for the number of new cases and the number of COVID-19 patients admitted to ICUs in the Metropolitan Region in Chile.

Effects of test timing and isolation length to reduce the risk of COVID-19 infection associated with airplane travel, as determined by infectious disease dynamics modeling.

Effective measures to reduce the risk of coronavirus disease 2019 (COVID-19) infection in overseas travelers are urgently needed. However, the effectiveness of current testing and isolation protocols is not yet fully understood. Here, we examined how the timing of testing and the number of tests conducted affect the spread of COVID-19 infection associated with airplane travel. We used two mathematical models of infectious disease dynamics to examine how different test protocols changed the density of infected individuals traveling by airplane and entering another country. We found that the timing of testing markedly affected the spread of COVID-19 infection. A single test conducted on the day before departure was the most effective at reducing the density of infected individuals travelling; this effectiveness decreased with increasing time before departure. After arrival, immediate testing was found to overlook individuals infected on the airplane. With respect to preventing infected individuals from entering the destination country, isolation with a single test on day 7 or 8 after arrival was comparable with isolation only for 11 or 14 days, respectively, depending on the model used, indicating that isolation length can be shortened with appropriately timed testing.

Assessing the Impact of (Self)-Quarantine through a Basic Model of Infectious Disease Dynamics.

We introduce a system of differential equations to assess the impact of (self-)quarantine of symptomatic infectious individuals on disease dynamics. To this end we depart from using the classic bilinear infection process, but remain within the framework of the mass-action assumption. From the mathematical point of view, the model we propose is interesting due to the lack of continuous differentiability at disease-free steady states, which implies that the basic reproductive number cannot be computed following established mathematical approaches for certain parameter values. However, we parametrise our mathematical model using published values from the COVID-19 literature, and analyse the model simulations. We also contrast model simulations against publicly available COVID-19 test data, focusing on the first wave of the pandemic during March-July 2020 in the UK. Our simulations indicate that actual peak case numbers might have been as much as 200 times higher than the reported positive test cases during the first wave in the UK. We find that very strong adherence to self-quarantine rules yields (only) a reduction of 22% of peak numbers and delays the onset of the peak by approximately 30-35 days. However, during the early phase of the outbreak, the impact of (self)-quarantine is much more significant. We also take into account the effect of a national lockdown in a simplistic way by reducing the effective susceptible population size. We find that, in case of a 90% reduction of the effective susceptible population size, strong adherence to self-quarantine still only yields a 25% reduction of peak infectious numbers when compared to low adherence. This is due to the significant number of asymptomatic infectious individuals in the population.

Scenario prediction of public health emergencies using infectious disease dynamics model and dynamic Bayes.

This study was aimed to discuss the predictive value of infectious disease dynamics model (IDD model) and dynamic Bayesian network (DBN) for scenario deduction of public health emergencies (PHEs). Based on the evolution law of PHEs and the meta-scenario representation of basic knowledge, this study established a DBN scenario deduction model for scenario deduction and evolution path analysis of PHEs. At the same time, based on the average field dynamics model of the SIR network, the dimensionality reduction process was performed to calculate the epidemic scale and epidemic time based on the IDD model, so as to determine the calculation methods of threshold value and epidemic time under emergency measures (quarantine). The Corona Virus Disease (COVID) epidemic was undertaken as an example to analyze the results of DBN scenario deduction, and the infectious disease dynamics model was used to analyze the number of reproductive numbers, peak arrival time, epidemic time, and latency time of the COVID epidemic. It was found that after the M1 measure was used to process the S1 state, the state probability and the probability of being true (T) were the highest, which were 91.05 and 90.21, respectively. In the sixth stage of the development of the epidemic, the epidemic had developed to level 5, the number of infected people was about 26, and the estimated loss was about 220 million yuan. The comprehensive cumulative foreground (CF) values of O1  ∼  O3 schemes were -1.34, -1.21, and -0.77, respectively, and the final CF values were -1.35, 0.01, and -0.08, respectively. The final CF value of O2 was significantly higher than the other two options. The household infection probability was the highest, which was 0.37 and 0.35 in Wuhan and China, respectively. Under the measures of home quarantine, the numbers of confirmed cases of COVID in China and Wuhan were 1.503 (95% confidential interval (CI) = 1.328  ∼  1.518) and 1.729 (95% CI = 1.107  ∼  1.264), respectively, showing good fits with the real data. On the 21st day after the quarantine measures were taken, the number of COVID across the country had an obvious peak, with the confirmed cases of 24495, and the model prediction value was 24085 (95% CI = 23988  ∼  25056). The incubation period 1/q was shortened from 8 days to 3 days, and the number of confirmed cases showed an upward trend. The peak period of confirmed cases was advanced, shortening the overall epidemic time. It showed that the prediction results of scenario deduction based on DBN were basically consistent with the actual development scenario and development status of the epidemic. It could provide corresponding decisions for the prevention and control of COVID based on the relevant parameters of the infectious disease dynamic model, which verified the rationality and feasibility of the scenario deduction method proposed in this study.

Controlling emerging zoonoses at the animal-human interface.

BACKGROUND: For many emerging or re-emerging pathogens, cases in humans arise from a mixture of introductions (via zoonotic spillover from animal reservoirs or geographic spillover from endemic regions) and secondary human-to-human transmission. Interventions aiming to reduce incidence of these infections can be focused on preventing spillover or reducing human-to-human transmission, or sometimes both at once, and typically are governed by resource constraints that require policymakers to make choices. Despite increasing emphasis on using mathematical models to inform disease control policies, little attention has been paid to guiding rational disease control at the animal-human interface. METHODS: We introduce a modeling framework to analyze the impacts of different disease control policies, focusing on pathogens exhibiting subcritical transmission among humans (i.e. pathogens that cannot establish sustained human-to-human transmission). We quantify the relative effectiveness of measures to reduce spillover (e.g. reducing contact with animal hosts), human-to-human transmission (e.g. case isolation), or both at once (e.g. vaccination), across a range of epidemiological contexts. RESULTS: We provide guidelines for choosing which mode of control to prioritize in different epidemiological scenarios and considering different levels of resource and relative costs. We contextualize our analysis with current zoonotic pathogens and other subcritical pathogens, such as post-elimination measles, and control policies that have been applied. CONCLUSIONS: Our work provides a model-based, theoretical foundation to understand and guide policy for subcritical zoonoses, integrating across disciplinary and species boundaries in a manner consistent with One Health principles.

Potential impact of individual exposure histories to endemic human coronaviruses on age-dependent severity of COVID-19.

BACKGROUND: Cross-reactivity to SARS-CoV-2 from exposure to endemic human coronaviruses (eHCoV) is gaining increasing attention as a possible driver of both protection against infection and COVID-19 severity. Here we explore the potential role of cross-reactivity induced by eHCoVs on age-specific COVID-19 severity in a mathematical model of eHCoV and SARS-CoV-2 transmission. METHODS: We use an individual-based model, calibrated to prior knowledge of eHCoV dynamics, to fully track individual histories of exposure to eHCoVs. We also model the emergent dynamics of SARS-CoV-2 and the risk of hospitalisation upon infection. RESULTS: We hypothesise that primary exposure with any eHCoV confers temporary cross-protection against severe SARS-CoV-2 infection, while life-long re-exposure to the same eHCoV diminishes cross-protection, and increases the potential for disease severity. We show numerically that our proposed mechanism can explain age patterns of COVID-19 hospitalisation in EU/EEA countries and the UK. We further show that some of the observed variation in health care capacity and testing efforts is compatible with country-specific differences in hospitalisation rates under this model. CONCLUSIONS: This study provides a "proof of possibility" for certain biological and epidemiological mechanisms that could potentially drive COVID-19-related variation across age groups. Our findings call for further research on the role of cross-reactivity to eHCoVs and highlight data interpretation challenges arising from health care capacity and SARS-CoV-2 testing.

A single holiday was the turning point of the COVID-19 policy of Israel.

OBJECTIVES: Despite an initial success, Israel's quarantine-isolation COVID-19 policy has abruptly collapsed. This study's aim is to identify the causes that led to this exponential rise in the accumulation of confirmed cases. METHODS: Epidemiological investigation reports were used to reconstruct chains of transmission as well as assess the net contribution of local infections relative to imported cases, infected travelers arriving from abroad. A mathematical model was implemented in order to describe the efficiency of the quarantine-isolation policy and the inflow of imported cases. The model's simulations included two scenarios for the actual time series of the symptomatic cases, providing insights into the conditions that lead to the abrupt change. RESULTS: The abrupt change followed a Jewish holiday, Purim, in which many public gatherings were held. According to the first scenario, the accumulation of confirmed cases before Purim was driven by imported cases resulting in a controlled regime, with an effective reproduction number, Re, of 0.69. In the second scenario, which followed Purim, a continuous rise of the local to imported cases ratio began, which led to an exponential growth regime characterized by an Re of 4.34. It was found that the change of regime cannot be attributed to super-spreader events, as these consisted of approximately 5% of the primary cases, which resulted in 17% of the secondary cases. CONCLUSIONS: A general lesson for health policymakers should be that even a short lapse in public responsiveness can lead to dire consequences.

Optimal Control of the COVID-19 Pandemic with Non-pharmaceutical Interventions.

The COVID-19 pandemic has forced societies across the world to resort to social distancing to slow the spread of the SARS-CoV-2 virus. Due to the economic impacts of social distancing, there is growing desire to relax these measures. To characterize a range of possible strategies for control and to understand their consequences, we performed an optimal control analysis of a mathematical model of SARS-CoV-2 transmission. Given that the pandemic is already underway and controls have already been initiated, we calibrated our model to data from the USA and focused our analysis on optimal controls from May 2020 through December 2021. We found that a major factor that differentiates strategies that prioritize lives saved versus reduced time under control is how quickly control is relaxed once social distancing restrictions expire in May 2020. Strategies that maintain control at a high level until at least summer 2020 allow for tapering of control thereafter and minimal deaths, whereas strategies that relax control in the short term lead to fewer options for control later and a higher likelihood of exceeding hospital capacity. Our results also highlight that the potential scope for controlling COVID-19 until a vaccine is available depends on epidemiological parameters about which there is still considerable uncertainty, including the basic reproduction number and the effectiveness of social distancing. In light of those uncertainties, our results do not constitute a quantitative forecast and instead provide a qualitative portrayal of possible outcomes from alternative approaches to control.