A cluster-based model of COVID-19 transmission dynamics.

Many countries have manifested COVID-19 trajectories where extended periods of constant and low daily case rate suddenly transition to epidemic waves of considerable severity with no correspondingly drastic relaxation in preventive measures. Such solutions are outside the scope of classical epidemiological models. Here, we construct a deterministic, discrete-time, discrete-population mathematical model called cluster seeding and transmission model, which can explain these non-classical phenomena. Our key hypothesis is that with partial preventive measures in place, viral transmission occurs primarily within small, closed groups of family members and friends, which we label as clusters. Inter-cluster transmission is infrequent compared with intra-cluster transmission but it is the key to determining the course of the epidemic. If inter-cluster transmission is low enough, we see stable plateau solutions. Above a cutoff level, however, such transmission can destabilize a plateau into a huge wave even though its contribution to the population-averaged spreading rate still remains small. We call this the cryptogenic instability. We also find that stochastic effects when case counts are very low may result in a temporary and artificial suppression of an instability; we call this the critical mass effect. Both these phenomena are absent from conventional infectious disease models and militate against the successful management of the epidemic.

A new approach to the dynamic modeling of an infectious disease

In this work we propose a delay differential equation as a lumped parameter or compartmental infectious disease model featuring high descriptive and predictive capability, extremely high adaptability and low computational requirement. Whereas the model has been developed in the context of COVID-19, it is general enough to be applicable with such changes as necessary to other diseases as well. Our fundamental modeling philosophy consists of a decoupling of public health intervention effects, immune response effects and intrinsic infection properties into separate terms. All parameters in the model are directly related to the disease and its management;we can measure or calculate their values a priori basis our knowledge of the phenomena involved, instead of having to extrapolate them from solution curves. Our model can accurately predict the effects of applying or withdrawing interventions, individually or in combination, and can quickly accommodate any newly released information regarding, for example, the infection properties and the immune response to an emerging infectious disease. After demonstrating that the baseline model can successfully explain the COVID-19 case trajectories observed all over the world, we systematically show how the model can be expanded to account for heterogeneous transmissibility, detailed contact tracing drives, mass testing endeavours and immune responses featuring different combinations of temporary sterilizing immunity, severity-reducing immunity and antibody dependent enhancement. [ABSTRACT FROM AUTHOR] Copyright of Mathematical Modelling of Natural Phenomena is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A new delay differential equation model for COVID-19

In this work we give a delay differential equation, the retarded logistic equation, as a mathematical model for the global transmission of COVID-19. This model accounts for asymptomatic carriers, pre-symptomatic or latent transmission as well as contact tracing and quarantine of suspected cases. We find that the equation admits varied classes of solutions including self-burnout, progression to herd immunity and multiple states in between. We use the term “partial herd immunity” to refer to these states, where the disease ends at an infection fraction which is not negligible but is significantly lower than the conventional herd immunity threshold. We believe that the spread of COVID-19 in every localized area can be explained by one of our solution classes. © 2020, Copyright held by the author(s).

Public health implications of a delay differential equation model for COVID 19

This paper describes the strategies derived from a novel delay differential equation model[1], signifying a practical extension of our recent work. COVID -19 is an extremely ferocious and an unpredictable pandemic which poses unique challenges for public health authorities, on account of which “case races” among various countries and states do not serve any purpose and present delusive appearances while ignoring significant determinants. We aim to propose comprehensive planning guidelines as a direct implication of our model. Our first consideration is reopening, followed by effective contact tracing and ensuring public compliance. We then discuss the implications of the mathematical results on people's behavior and eventually provide conclusive points aimed at strengthening the arsenal of resources that are helpful in framing public health policies. The knowledge about pandemic and its association with public health interventions is documented in the various literature-based sources. In this study, we explore those resources to explain the findings inferred from delay differential equation model of covid-19. © 2020, Copyright held by the author(s).

Impact of reproduction number on the multiwave spreading dynamics of COVID-19 with temporary immunity: A mathematical model.

OBJECTIVES: The recent discoveries of phylogenetically confirmed COVID-19 reinfection cases worldwide, together with studies suggesting that antibody titres decrease over time, raise the question of what course the epidemic trajectories may take if immunity were really to be temporary in a significant fraction of the population. The objective of this study is to obtain an answer for this important question. METHODS: We construct a ground-up delay differential equation model tailored to incorporate different types of immune response. We considered two immune responses: (a) short-lived immunity of all types, and (b) short-lived sterilizing immunity with durable severity-reducing immunity. RESULTS: Multiple wave solutions to the model are manifest for intermediate values of the reproduction number R; interestingly, for sufficiently low as well as sufficiently high R, we find conventional single-wave solutions despite temporary immunity. CONCLUSIONS: The versatility of our model, and its very modest demands on computational resources, ensure that a set of disease trajectories can be computed virtually on the same day that a new and relevant immune response study is released. Our work can also be used to analyse the disease dynamics after a vaccine is certified for use and information regarding its immune response becomes available.