Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model directly related to epidemiological data. We derive some analytical results, as well as perform numerical simulations. We use the proposed model to analyze COVID-19 epidemic data in Armenia. We propose a strategy: organize a quarantine, and then conduct extensive testing of risk groups during the quarantine, evaluating the percentage of the population among risk groups and people with symptoms.
In this work, we have developed a Coxian distributed SEIR model in incorporating an empirical incubation period. We show that the global dynamics are completely determined by a basic reproduction number. An application of the Coxian distributed SEIR model using data of an empirical incubation period is explored. The model may be useful for resolving causing the realistic intrinsic parts in classical epidemic models since Coxian distribution approximately converges to any distribution.
The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-f…
To reduce the biases of traditional survey-based methods, this paper proposes an epidemic model-based approach to inference the incubation period distribution of COVID-19 utilizing the publicly reported confirmed case number. We construct an epidemic model, namely SEAIR, and take advantage of the dynamic transmission process depicted by SEAIR to estimate the onset probability in each day of exposed individuals in eight impacted countries. Based on these estimations, the general incubation probability distribution of COVID-19 has been revealed. The proposed method can avoid several biases of tr…
An epidemic disease caused by a new coronavirus has spread in Northern Italy with a strong contagion rate. We implement an SEIR model to compute the infected population and number of casualties of this epidemic. The example may ideally regard the situation in the Italian Region of Lombardy, where the epidemic started on February 25. We calibrate the model with the number of dead individuals to date (May 5, 2020) and constraint the parameters on the basis of values reported in the literature. The peak occurs at day 37 (March 31) approximately, when there is a rapid decrease, with a reproduction…
The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms. For typhoid fever, polio, measles, leukemia and many other diseases, the incubation period is highly variable. Some affected people take much longer than average to show symptoms, leading to a distribution of incubation periods that is right skewed and often approximately lognormal. Although this statistical pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here we propose an explanation based on evolutionary dynamics on graphs. F…
We analyzed the first 255 PCR-confirmed cases of monkeypox occurred in Italy in 2022. Preliminary estimates indicate: mean incubation period of 9.1 days (95%CI of the mean: 6.5-10.9); mean generation time of 12.5 days (95%CI of the mean: 7.5-17.3); reproduction number in the MSM community of 2.43 (95%CI: 1.82-3.26).
With the launch of second line anti-retroviral therapy for HIV infected individuals, there has been an increased expectation on surviving period of people with HIV. We consider previously well-known models in HIV epidemiology where the parameter for incubation period is used as one of the important components to explain the dynamics of the variables. Such models are extended here to explain the dynamics with respect to a given therapy that prolongs life of an HIV infected individual. A deconvolution method is demonstrated for estimation of parameters in the situations when no-therapy and multi…
Background. During 2021, the COVID-19 pandemic was characterized by the emergence of lineages with increased fitness. For most of these variants, quantitative information is scarce on epidemiological quantities such as the incubation period and generation time, which are critical for both public health decisions and scientific research. Method. We analyzed a dataset collected during contact tracing activities in the province of Reggio Emilia, Italy, throughout 2021. We determined the distributions of the incubation period using information on negative PCR tests and the date of last exposure fr…
The origin of the unusual incubation period distribution in the development of AIDS is largely unresolved. A key factor in understanding the observed distribution of latency periods, as well as the occurrence of infected individuals not developing AIDS at all, is the dynamics of the long lasting struggle between HIV and the immune system. Using a computer simulation, we study the diversification of viral genomes under mutation and the selective pressure of the immune system.In common infections vast spreading of viral genomes usually does not takes place. In the case of an HIV infection this m…
A pandemic caused by a new coronavirus (COVID-19) has spread worldwide, inducing an epidemic still active in Argentina. In this chapter, we present a case study using an SEIR (Susceptible-Exposed-Infected-Recovered) diffusion model of fractional order in time to analyze the evolution of the epidemic in Buenos Aires and neighboring areas (Región Metropolitana de Buenos Aires, (RMBA)) comprising about 15 million inhabitants. In the SEIR model, individuals are divided into four classes, namely, susceptible (S), exposed (E), infected (I) and recovered (R). The SEIR model of fractional order allows…
Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the approach of Harko et al. (2014) is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The SEIR model curves have nearly the same shapes as the SIR ones, but with a stretch factor applied to them across time that is related to the ratio of the incubation to infectious periods. This finding…
For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number, and consequently to a larger epidemic outbreak, when the mean infectious period is fixed. We discuss how this result is related to various stochastic orderings of the distributions of infectious periods. The results are illustrated by a number of explicit stochastic simulations, suggesting that their validity goes beyond regular networks…
Absent a drug or vaccine, containing epidemic outbreaks is achieved by means of social distancing, specifically mobility restrictions and lock-downs. Such measures impose a hurtful toll on the economy, and are difficult to sustain for extended periods. As an alternative, we propose here an alternating quarantine strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and quarantine. This regime affords a dual partition:\ half of the population interacts for only…
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases.
The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise, message passing, and spatial models as special cases. For this model, we prove a monotonic relationship between the variability of the infectious period (with fixed mean) and the probability that the infection will reach any given subset of the population by any given time. For certain families of distributions, this result implies that epidemic severity is decrea…
Without vaccines and treatments, societies must rely on non-pharmaceutical intervention strategies to control the spread of emerging diseases such as COVID-19. Though complete lockdown is epidemiologically effective, because it eliminates infectious contacts, it comes with significant costs. Several recent studies have suggested that a plausible compromise strategy for minimizing epidemic risk is periodic closure, in which populations oscillate between wide-spread social restrictions and relaxation. However, no underlying theory has been proposed to predict and explain optimal closure periods …
We investigate epidemic models with spatial structure based on the cellular automata method. The construction of the cellular automata is from the study by Weimar and Boon about the reaction-diffusion equations [Phys. Rev. E 49, 1749 (1994)]. Our results show that the spatial epidemic models exhibit the spontaneous formation of irregular spiral waves at large scales within the domain of chaos. Moreover, the irregular spiral waves grow stably. The system also shows a spatial period-2 structure at one dimension outside the domain of chaos. It is interesting that the spatial period-2 structure wi…
Malaria is a major contributor to health burdens throughout the regions where it is endemic. Historically, it was believed that there was limited morbidity and essentially no mortality associated with Plasmodium vivax; however, evidence from diverse settings now suggests that infections with P. vivax can be both severe and fatal. This awareness has highlighted a critical gap: the vast majority of research has been directed towards P. falciparum, leading to a decades-long neglect of epidemiological and clinical studies of P. vivax. There exists a large body of historical data on human experimen…
While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enfor…
This paper presents a compact pairwise model that describes the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian models with exponentially distributed infectious period and epidemics with a constant infectious period. We show how the compact approach leads to a system of equations whose size is independent of the range of node degrees, thus significantly reducing the complexity of the model. Network clustering is incorporated into the model to provide a more accurate repres…
Our paper investigates distributions of exposed and infectious time periods in an epidemic model and how applying a disease control strategy affects the model's accuracy. While ordinary differential equations are widely used for their simplicity, they incorporate an exponential distribution for time spent exposed or infectious. This allows for a high probability of unrealistically short exposed and infectious time periods. We propose that caution must be taken when applying intervention methods to basic models in order to avoid inaccurate predictions. Delay differential equations, which use a …
The transmission of vector infectious diseases, which produces complex spatiotemporal patterns, is analyzed by a periodically forced two-dimensional cellular automata model. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult and immature vector populations. The dynamics includes external seasonality forcing (rainfall intensity data), human and mosquito mobility, and vector control effec…
The data of the 2009 A(H1N1) epidemic in Istanbul, Turkey is unique in terms of the collected data, which include not only the hospitalization but also the fatality information recorded during the pandemic. The analysis of this data displayed an unexpected time shift between the hospital referrals and fatalities. This time shift, which does not conform to the SIR and SEIR models, was explained by multi-stage SIR and SEIR models [21]. In this study we prove that the delay for these models is half of the infectious period within a quadratic approximation, and we determine the epidemic parameters…
Network epidemiology often assumes that the relationships defining the social network of a population are static. The dynamics of relationships is only taken indirectly into account, by assuming that the relevant information to study epidemic spread is encoded in the network obtained by considering numbers of partners accumulated over periods of time roughly proportional to the infectious period of the disease at hand. On the other hand, models explicitly including social dynamics are often too schematic to provide a reasonable representation of a real population, or so detailed that no genera…
We propose a stochastic SIR model, specified as a system of stochastic differential equations, to analyse the data of the Italian COVID-19 epidemic, taking also into account the under-detection of infected and recovered individuals in the population. We find that a correct assessment of the amount of under-detection is important to obtain reliable estimates of the critical model parameters. Moreover, a single SIR model over the whole epidemic period is unable to correctly describe the behaviour of the pandemic. Then, the adaptation of the model in every time-interval between relevant governmen…
Attempts to curb the spread of coronavirus by introducing strict quarantine measures apparently have different effect in different countries: while the number of new cases has reportedly decreased in China and South Korea, it still exhibit significant growth in Italy and other countries across Europe. In this brief note, we endeavour to assess the efficiency of quarantine measures by means of mathematical modelling. Instead of the classical SIR model, we introduce a new model of infection progression under the assumption that all infected individual are isolated after the incubation period in …
Ross-Macdonald models are the building blocks of most vector-borne disease models. Even for the same disease, different authors use different model formulations, but a study of the dynamical consequences of assuming different hypotheses is missing. In this work we present different formulations of the basic Ross-Macdonald model together with a careful discussion of the assumptions behind each model. The most general model presented is an agent based model for which arbitrary distributions for latency and infectious periods for both, host and vectors, is considered. At population level we also …
In this paper, we study the interplay between individual behaviors and epidemic spreading in a dynamical network. We distribute agents on a square-shaped region with periodic boundary conditions. Every agent is regarded as a node of the network and a wireless link is established between two agents if their geographical distance is less than a certain radius. At each time, every agent assesses the epidemic situation and make decisions on whether it should stay in or leave its current place. An agent will leave its current place with a speed if the number of infected neighbors reaches or exceeds…
The goal of this study is to establish a general framework for predicting the so-called critical Turning Period in an infectious disease epidemic such as the COVID-19 outbreak in China early this year. This framework enabled a timely prediction of the turning period when applied to Wuhan COVID-19 epidemic and informed the relevant authority for taking appropriate and timely actions to control the epidemic. It is expected to provide insightful information on turning period for the world's current battle against the COVID-19 pandemic. The underlying mathematical model in our framework is the ind…
In this article, we develop a data assimilation procedure to predict the evolution of epidemics with data uncertainty, with application to the Covid-19 pandemic. We construct a vademecum of solutions by solving the SIR epidemic model for a set of data neighboring the estimated real (or official) ones. A reduced basis is constructed from this vademecum through Proper Orthogonal Decomposition (POD). The reduced POD base is then applied to assimilate the pandemic data (infected, recovered, deceased) during the period in which data are known, by a least squares procedure. The fitted curves are the…
Which nodes are most vulnerable to an epidemic spreading through a network, and which carry the highest risk of causing a major outbreak if they are the source of the infection? Here we show how these questions can be answered to good approximation using the cavity method. Several curious properties of node vulnerability and risk are explored: some nodes are more vulnerable than others to weaker infections, yet less vulnerable to stronger ones; a node is always more likely to be caught in an outbreak than it is to start one, except when the disease has a deterministic lifetime; the rank order …
We study and predict the evolution of Covid-19 in six US states from the period May 1 through August 31 using a discrete compartment-based model and prescribe active intervention policies, like lockdowns, on the basis of minimizing a loss function, within the broad framework of partially observed Markov decision processes. For each state, Covid-19 data for 40 days (starting from May 1 for two northern states and June 1 for four southern states) are analyzed to estimate the transition probabilities between compartments and other parameters associated with the evolution of the epidemic. These qu…
