A novel deterministic forecast model for the Covid-19 epidemic based on a single ordinary integro-differential equation

Abstract

In this paper, we present a new approach to deterministic modelling of COVID-19 epidemic. Our model dynamics is expressed by a single prognostic variable which satisfies an integro-differential equation. All unknown parameters are described with a single, timedependent variable R(t). We show that our model has similarities to classic compartmental models, such as SIR, and that the variable R(t) can be interpreted as a generalized effective reproduction number. The advantages of our approach are the simplicity of having only one equation, the numerical stability due to an integral formulation and the reliability since the model is formulated in terms of the most trustable statistical data variable: the number of cumulative diagnosed positive cases of COVID-19. Once this dynamic variable is calculated, other non-dynamic variables, such as the number of heavy cases (hospital beds), the number of intensive-care cases (ICUs) and the fatalities, can be derived from it using a similarly stable, integral approach. The formulation with a single equation allows us to calculate from real data the values of the sample effective reproduction number, which can then be fitted. Extrapolated values of R(t) can be used in the model to make reliable forecasts, though under the assumption that measures for reducing infections are maintained. We have applied our model to more than 15 countries and the ongoing results are available on a web-based platform [1]. In this paper, we focus on the data for two exemplary countries, Italy and Germany, and show that the model is capable of reproducing the course of the epidemic in the past and forecasting its course for a period of four to five weeks with a reasonable numerical stability.

Multi-state SVIRD Model with Continuous-time Markov Chain Assumption on the Spread of Infectious Diseases

“…The types of infectious disease modeling consist of deterministic, stochastic, and phenomenological models. Classical deterministic modeling has been widely used, including by Triampo, Baowan, Tang, Nuttavut, and Doungchawee (2007); Köhler-Rieper, Röhl, and De Micheli (2020), then a comparison between deterministic and stochastic was developed by Olabode, Culp, Fisher, Tower, Hull-Nye, and Wang (2021); Allen and Burgin (2000) to interpret various epidemic models. Meanwhile, the phenomenological model has been developed in previous studies using the logistic growth model and the expansion of the Richards curve model Rosadi (2020, 2022a,b).…”

A discrete model for the evaluation of public policies: The case of Colombia during the COVID-19 pandemic

“…We identified several attempts to propose and apply models with mathematical expressions. These includes classical compartmental models [ 12 ] alongside Erlang models [ 13 ], integrodifferential equations to simulate infection process [ 14 , 15 ], delay-differential equations to include latency period [ 16 ], partial differential equations for spatial heterogeneity [ 17 , 18 ], and meta-populations for age-directed control strategies [ 19 ]. Also, we found that there are several mathematical models formulated in multiple countries to understand the complex transmission pattern of the COVID-19 pandemic [ 12 ].…”

Impact of control interventions on COVID-19 population dynamics in Malaysia: a mathematical study

“…A deterministic model based on SIR framework was proposed to understand the evolution of COVID-19 outbreaks during lockdown and social distancing policy in Germany and Italy by Ianni and Rossi [ 57 ]. Similarly, Köhler-Rieper et al [ 58 ] proposed a new approach to mathematical modelling of COVID-19 transmission dynamics by constructing a single ordinary integro-differential equation. It was shown that the model has similarities with the classical SIR model, and capable of predicting the disease outbreaks for a period of about 4 weeks.…”