Narrow Results

We analyze a spatial susceptible-infected epidemic model using cellular automata and investigate the relations between the power-law distribution of patch sizes and the regime of invasion. The obtained results show that, when the invasion is in the form of coexistence of stable target and spiral wave, power-law will emerge, which may provide a new insight into the control of disease.

As one of the most densely populated countries in the world, Bangladesh has been trying to contain the impact of a pandemic like coronavirus disease 2019 (COVID-19) since March, 2020. Although government announced an array of restricted measures to slow down the diffusion in the beginning of the pandemic, the lockdown has been lifted gradually by reopening all the industries, markets and offices with a notable exception of educational institutes. As the physical geography of Bangladesh is highly variable across the largest delta, the population of different regions and their lifestyle also differ in the country. Thus, to get the real scenario of the current pandemic and a possible second wave of COVID-19 transmission across Bangladesh, it is essential to analyze the transmission dynamics over the individual districts. In this paper, we propose to integrate the Unscented Kalman Filter (UKF) with classic SIRD model to explain the epidemic evolution of individual districts in the country. We show that UKF-SIRD model results in a robust prediction of the transmission dynamics for 1–4 months. Then we apply the robust UKF-SIRD model over different regions in Bangladesh to estimates the course of the epidemic. Our analysis demonstrates that in addition to the densely populated areas, industrial areas and popular tourist spots will be in the risk of higher COVID-19 transmission if a second wave of COVID-19 occurs in the country. In the light of these outcomes, we also provide a set of suggestions to contain the future pandemic in Bangladesh.

A formal approach to modeling the expansion of natural events is presented in this paper. Since the mathematical, statistical or computational methods used are not relevant for development, a modular framework is carried out that guides from the external observation down to the innermost level of the variables that have to appear in the future mathematical-computational formalization. As an example we analyze the expansion of Covid-19. We perform a qualitative estimation of the impact of the causes on the delays of the spread and an analysis of the parameters.

We show that the behavior of an epidemiology model depends sensitively on the shortcut density in the shortcut network. This is consistent with an earlier work on other processes on the shortcut network. We analytically study the reason for the sensitivity. The shortcut network is similar to the small world network, and it has the advantage that the model dependence on the shortcut density can be analytically studied. The model would be relevant to the spread of diseases in human, animal, plant or other populations, to the spread of viruses in computer networks, or to the spread of social contagion in social networks. It would also be relevant in understanding the variations in the load on routers connecting different computer networks, as the network topology gets extended by the addition of new links, and in analyzing the placement of certain special sensors in a sensor network laid out in a non-random way with some shortcut links.

In this study, we consider the dynamics of the Babesiosis transmission on bovine populations and ticks. The most important role in the transmission of the parasite is the ticks from the Ixodidae family. The vector tick takes factors (merozoites in erythrocytes) from the diseased animal while sucking the blood. To model and investigate the transmissions of this parasite and address this important issue, we have considered the disease in a fractional epidemiological model. This paper, therefore, discusses the mechanisms of transmission of Babesiosis defined in the fractional derivative sense. The Caputo–Fabrizio (CF) derivative is considered to study the propagation mechanisms of Babesiosis. First, the important characteristics of the model have been presented, and then the transmission of the Babesiosis model defined in CF is discussed. The application of fixed-point theory is used to derive the concept of the qualitative properties of the mentioned model. The solution is obtained by using the Homotopy perturbation Elzaki transform method (HPETM). Numerical simulations are performed, and the effects of the arbitrary-order derivatives are investigated graphically.

We study the predictability of epidemic forecasts in a data-driven meta-population model considering the complete air transportation system and the associated urban areas. We define the predictability as the robustness of the system evolution with respect to the stochastic fluctuations. As a quantitative measure of predictability we consider the information similarity of the time series characterizing different epidemic outbreaks with the same initial conditions. We study the predictability as a function of the parameters describing the basic susceptible-latent-infected and recovered disease dynamics. We find that the overall predictability is determined by the level of sampling of the underlying travel pattern by infected and latent individuals.

We present a time-delayed SIS model on complex networks to study epidemic spreading. We found that the existence of delay will affect, and oftentimes enhance, both outbreak and prevalence of infectious diseases in the networks. For small-world networks, we found that the epidemic threshold and the delay time have a power-law relation. For scale-free networks, we found that for a given transmission rate, the epidemic prevalence has an exponential form, which can be analytically obtained, and it decays as the delay time increases. We confirm all results by sufficient numerical simulations.

Modeling the dynamics of persistent infections presents several challenges. These diseases are characterized by long latency periods, which makes it compulsory to consider populations of varying sizes. In this paper, we discuss a model for the spreading of persistent infections in homogeneous, well-mixed, populations. We first derive the equations describing the system's dynamics and find the epidemic threshold by a stability analysis. Analytical solutions are then shown to agree with results obtained with numerical simulations. The present model, although simple, opens the path to more complex approaches to the spreading of persistent infections.

A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behavior observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose, we introduce, in a naïve discrete-time SIRS model, seasonal variability (i) in the loss of immunity and (ii) in the infection probability, modeled by sequences of kicks. Effects of a variable population size (assumed as logistic) are also analyzed. Restrictive assumptions are made on the parameters of the models, in order to guarantee that the transitions are determined by true probabilities, so that comparisons with stochastic discrete-time previsions can be also provided. Numerical simulations show that the characteristics of real infectious diseases can be adequately modeled.

We study the propagation of a disease in a population where agents are characterized by their awareness level, representing the measures they take to avoid the infection. We introduce another agent, the government, which is constantly sending a message to the population trying to steer the mean awareness to a value which should ensure the extinction of the disease. We propose three levels to analyze this model. First, an agent-based model, which we use later to derive a mean-field system of ordinary differential equations; and finally, we propose a kinetic approach to model the evolution of the distribution of agents on the awareness levels. We obtain nonlinear systems of different dimension, first an ODE-Boltzmann system and later an ODEs-PDE system, where a Boltzmann or a first order, non-local partial differential equation are coupled with two ordinary differential equations that describe the evolution of the epidemic and the response of the government. We prove the existence and uniqueness of solutions in an abstract setting. Finally, we consider stubborn agents that are not willing to apply protection measures.

The COVID-19 pandemic lit a fire under researchers who have subsequently raced to build models which capture various physical aspects of both the biology of the virus and its mobility throughout the human population. These models could include characteristics such as different genders, ages, frequency of interactions, mutation of virus, etc. Here, we propose two mathematical formulations to include virus mutation dynamics. The first uses a compartmental epidemiological model coupled with a discrete-time finite-state Markov chain. If one includes a nonlinear dependence of the transition matrix on current infected, the model is able to reproduce pandemic waves due to different variants. The second approach expands such an idea to a continuous state-space leveraging a combination of ordinary differential equations with an evolution equation for measure. This approach allows to include reinfections with partial immunity with respect to variants genetically similar to that of first infection.

Many compartment based epidemiological models are written as differential equation systems for various status subpopulation sizes with per person-time transfer rates between compartments. However, field data obtained by sampling at chosen times is usually provided in terms of status proportions from the total observable population (e.g., relative prevalence). Relationships between per person-time transfer rates (incidence, mortality, intervention rates) and proportions are not obvious when heterogeneity is at work because the various subpopulation sizes undergo different attrition rates and are not evolving in synchrony with the corresponding proportions. Rules are proposed to write sets of differential equations for compartment models, directly in terms of the proportions of the total observable at any time. To facilitate the writing of relationships between per person-time transfer rates and proportions, the systems are cast in network equivalent forms satisfying rules analogous to those of electrical networks (Kirchhoff's law for currents). The method is also extended to variability in the rates within a status subpopulation, considering either a fixed set of compartmental subdivisions or an inner continuum of differences in rates.

A model for HIV transmission in homosexual populations is proposed taking into consideration different preventive attitudes, blood screening and effects of social networks. The equilibrium points of the system are calculated with and without blood screening and their stabilities are analyzed. By using these analytical results and numerical simulations, some evolving aspects of the epidemic are discussed.

Underreporting of HIV/AIDS cases is a common problem in HIV epidemiology which often skews epidemiologic projections on which public health policy decisions are often based, especially in the cases of low HIV prevalence countries or in early phases of an emerging epidemic when the HIV incidence is still low, but might be growing rapidly. In this work, we propose a simple mathematical model with groups of known and undetected HIV-positives. Using this model with the annual HIV incidence data of new HIV cases and new AIDS cases detected at onset of symptoms, we are able to obtain an estimate for the number of undetected HIV-positives. Moreover, using Taiwan data of 1993–2000, we are able to predict the number of new cases in the next two years within 5% accuracy. We also give an approximate ratio of underreporting which approximates the magnitude of underreporting of HIV cases in low HIV prevalence settings. The procedure is illustrated with the HIV data of Taiwan and Cuba. The result shows that underreporting in Cuba is low, probably due to its intense contact tracing program. For Taiwan, the level of underreporting is higher, but has improved slightly since 1999. The method is useful as a simple tool to gauge the immediate impact of an emerging epidemic, as well as for the purpose of public health policy planning and short-term future projections.

The effective reproduction number $R(t)$, the average number of secondary cases that are generated by a single primary case at calendar time $t$, plays a critical role in interpreting the temporal transmission dynamics of an infectious disease epidemic, while the case fatality risk (CFR) is an indispensable measure of the severity of disease. In many instances, $R(t)$ is estimated using the reported number of cases (i.e., the incidence data), but such report often does not arrive on time, and moreover, the rate of diagnosis could change as a function of time, especially if we handle diseases that involve substantial number of asymptomatic and mild infections and large outbreaks that go beyond the local capacity of reporting. In addition, CFR is well known to be prone to ascertainment bias, often erroneously overestimated. In this paper, we propose a joint estimation method of $R(t)$ and CFR of Ebola virus disease (EVD), analyzing the early epidemic data of EVD from March to October 2014 and addressing the ascertainment bias in real time. To assess the reliability of the proposed method, coverage probabilities were computed. When ascertainment effort plays a role in interpreting the epidemiological dynamics, it is useful to analyze not only reported (confirmed or suspected) cases, but also the temporal distribution of deceased individuals to avoid any strong impact of time dependent changes in diagnosis and reporting.

We attempt to model the circulation of the Feline Immunodeficiency Virus (FIV), a retrovirus analogous to the HIV, within populations of domestic cats. Domestic cats exhibit different patterns of population dynamics, social behaviour and reproductive strategies. In fact, cats can be either solitary or living in large social groups, with many intermediate states.

The aim of the presented model is to provide a conceptualization of the mechanisms of FIV spreading rather than to be a predictive tool. As one of our goals is to integrate easily new informations when available, and to remain simple and close to the biological reality, parameters, such as sex, age classes and dispersion, have been incorporated successively. This model can also be adapted to different types of cat populations by simple changes, as it could be to other host populations. A study of the stability of the model has been done. Based on available data, values of two parameters has been estimated: the carrying capacity and the transmission rate. Results are in good accordance with biological data.

Two different theoretical functions are proposed for the age-dependent transmission coefficients which takes into account the distribuitions of the contact probabilities between susceptible individuals of age a with infected individuals of age a′. A numerical simulation is presented with measles and rubella data from two distinct communities. The impact of control measures is also simulated using the assumed functions for the age-dependent transmission coefficients.

In order to understand, in terms of the epidemiology of a disease, the consequences of having a population which can recover from the disease back to a state of susceptibility and the additional effects of recovery to immunity, we have formulated and compared a series of models; each includes a biological feature known to occur in a real host-pathogen system. For example, vertical transmission of the disease or free living infective stages of the pathogen. Taken together, these models, in general, follow predictable patterns of behaviour. There are exceptions, but these can be explained in terms of some sort of density dependence or time delay written into the framework of the model.

We present a five-variable compartmental model for the spread of Trypanosoma brucei gambiense, the parasite responsible for the transmission (through tsetse flies) of sleeping sickness in Central Africa. The model’s equilibrium points depend on two “summary parameters”: g_r, the proportion removed among human infectives, and R₀, the basic reproduction rate. Stability results are obtained for the origin but not for other equilibrium points. A two-variable simplified version of the model is presented and the stability of all its equilibrium points can be investigated analytically. Both models are applied to the Niari focus of Central Africa and used to test the impact of a vector control strategy. The models’ results are in agreement with the extinction of the epidemic that was brought about by a fifty percent decrease in vector density.

The aim of this paper is to model corona-virus (COVID-19) taking into account random perturbations. The suggested model is composed of four different classes i.e. the susceptible population, the smart lockdown class, the infectious population, and the recovered population. We investigate the proposed problem for the derivation of at least one unique solution in the positive feasible region of nonlocal solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function and the condition for the extinction of the disease is also established. The obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been simulated numerically.