ABSTRACT
Much media and societal attention is today focused on how to best control the spread of coronavirus (COVID-19). Every day brings us new data, and policy makers are implementing different strategies in different countries to manage the impact of COVID-19. To respond to the first 'wave' of infection, several countries, including the UK, opted for isolation/lockdown initiatives, with different degrees of rigour. Data showed that these initiatives have yielded the expected results in terms of containing the rapid trajectory of the virus. When this article was first prepared (April 2020), the affected societies were wondering when the isolation/lockdown initiatives should be lifted. While detailed epidemiological, economic as well as social studies would be required to answer this question completely, here we employ a simple engineering model. Albeit simple, the model is capable of reproducing the main features of the data reported in the literature concerning the COVID-19 trajectory in different countries, including the increase in cases in countries following the initially successful isolation/lockdown initiatives. Keeping in mind the simplicity of the model, we attempt to draw some conclusions, which seem to suggest that a decrease in the number of infected individuals after the initiation of isolation/lockdown initiatives does not necessarily guarantee that the virus trajectory is under control. Within the limit of this model, it would seem that rigid isolation/lockdown initiatives for the medium term would lead to achieving the desired control over the spread of the virus. This observation seems consistent with the 2020 summer months, during which the COVID-19 trajectory seemed to be almost under control across most European countries. Consistent with the results from our simple model, winter 2020 data show that the virus trajectory was again on the rise. Because the optimal solution will achieve control over the spread of the virus while minimising negative societal impacts due to isolation/lockdown, which include but are not limited to economic and mental health aspects, the engineering model presented here is not sufficient to provide the desired answer. However, the model seems to suggest that to keep the COVID-19 trajectory under control, a series of short-to-medium term isolation measures should be put in place until one or more of the following scenarios is achieved: a cure has been developed and has become accessible to the population at large; a vaccine has been developed, tested and distributed to large portions of the population; a sufficiently large portion of the population has developed resistance to the COVID-19 virus; or the virus itself has become less aggressive. It is somewhat remarkable that an engineering model, despite all its approximations, provides suggestions consistent with advanced epidemiological models developed by several experts in the field. The model proposed here is however not expected to be able to capture the emergence of variants of the virus, which seem to be responsible for significant outbreaks, notably in India, in the spring of 2021, it cannot describe the effectiveness of vaccine strategies, as it does not differentiate among different age groups within the population, nor does it allow us to consider the duration of the immunity achieved after infection or vaccination.
ABSTRACT
In view of the fact that the existing propagation models ignore the influence of different fields and different virus variants on individual infection, and the classical propagation models only describe the macroscopic situation of virus transmission, which cannot be specific to individual cases, this paper proposes 67ya microscopic virus propagation model based on hypergraph (HC-SIRS). Firstly, the concept of hypergraph is used to divide different fields of individuals into corresponding hyperedges. Based on different contact probabilities of each hyperedge, the contact probability matrix is formed to relate the contact between individuals. The individual infection probability of micro-virus propagation model based on hypergraph is deduced, and the corresponding differential equation is established. Secondly, the basic regeneration number and its characteristics of the model are derived. The upper bound of the basic regeneration number of the model is less than or equal to that of the classical SIRS model, indicating that the virus is more difficult to spread in this model. In fact, the different fields people live in and the different personal constitutions have a certain impact on the spread of the virus. The model is more comprehensive, so it is more suitable for simulating the spread of the virus in theory. Finally, the COVID-19 data of Diamond Princess and two cities in China are used for simulation experiments, and the mean absolute error(MAE) is used as the evaluation standard. The results showed that HC-SIRS could well simulate the spread of COVID-19. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
ABSTRACT
In this manuscript, we investigate a novel Susceptible-Exposed-Infected-Quarantined-Recovered (SEIQR) COVID-19 propagation model with two delays, and we also consider supply chain transmission and hierarchical quarantine rate in this model. Firstly, we analyze the existence of an equilibrium, including a virus-free equilibrium and a virus-existence equilibrium. Then local stability and the occurrence of Hopf bifurcation have been researched by thinking of time delay as the bifurcation parameter. Besides, we calculate direction and stability of the Hopf bifurcation. Finally, we carry out some numerical simulations to prove the validity of theoretical results.