Traveling Waves in a Reaction-Diffusion Addiction Epidemic Model with Distributed Delays

How to incorporate social vulnerability into epidemic mathematical modelling: recommendations from an international Delphi.

With fast infectious diseases such as COVID-19, the SIR model may not represent the number of infections due to the occurrence of distribution shifts. In this study, we use simulations based on the SIR model to verify the prediction accuracy of new positive cases by considering distribution shifts. Instead of expressing the overall number of new positive cases in the SIR model, the number of new positive cases in a specific region is simulated, the expanded estimation ratio is expressed in the AR model, and these are multiplied to predict the overall number. In addition to the parameters used in the SIR model, we introduced parameters related to social variables. The parameters for the simulation were estimated daily from the data using approximate Bayesian computation (ABC). Using this method, the average absolute percent error in predicting the number of positive cases for the peak of the eighth wave (2022/12/22–12/28) for all of Japan was found to be 62.2% when using data up to two months before the peak and 6.2% when using data up to one month before the peak. Our simulations based on the SIR model reproduced the number of new positive cases across Japan and produced reasonable results when predicting the peak of the eighth wave.

Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination

An unprecedented upsurge of COVID-19-positive cases and deaths is currently being witnessed across India. According to WHO, India reported an average of 3.9 lakhs of new cases during the first week of May 2021 which equals 47% of new cases reported globally and 276 daily cases per million population. In this letter, the concept of SIR and fractal interpolation models is applied to predict the number of positive cases in India by approximating the epidemic curve, where the epidemic curve denotes the two-dimensional graphical representation of COVID-19-positive cases in which the abscissa denotes the time, while the ordinate provides the number of positive cases. In order to estimate the epidemic curve, the fractal interpolation method is implemented on the prescribed data set. In particular, the vertical scaling factors of the fractal function are selected from the SIR model. The proposed fractal and SIR model can also be explored for the assessment and modeling of other epidemics to predict the transmission rate. This letter investigates the duration of the second and third waves in India, since the positive cases and death cases of COVID-19 in India have been highly increasing for the past few weeks, and India is in a midst of a catastrophizing second wave. The nation is recording more than 120 million cases of COVID-19, but pandemics are still concentrated in most states. In order to predict the forthcoming trend of the outbreaks, this study implements the SIR and fractal models on daily positive cases of COVID-19 in India and its provinces, namely Delhi, Karnataka, Tamil Nadu, Kerala and Maharashtra.

We prove the global asymptotic stability of the disease-free and the endemic equilibrium for general SIR and SIRS models with nonlinear incidence. Instead of the popular Volterra-type Lyapunov functions, we use the method of Dulac functions, which allows us to extend the previous global stability results to a wider class of SIR and SIRS systems, including nonlinear (density-dependent) removal terms as well. We show that this method is useful in cases that cannot be covered by Lyapunov functions, such as bistable situations. We completely describe the global attractor even in the scenario of a backward bifurcation, when multiple endemic equilibria coexist.

The phenomenon of the spread of infectious disease can be formed as an epidemic model. Simplest epidemic model is SI model which can be extended to SIR and SIS model. If recover person will not be susceptible to same disease until the immunity dies out, then the model will be SIRS model. If all person in SIRS model are in population which have restrictiveness of carrying capacity, then it will be formed SIRS model with logistic growth. This model can be presented mathematically using a system of differential equations. Based on SIRS model with logistic growth, it is obtained three disease-free equilibrium points and one endemic equilibrium point. Two disease-free equilibrium points are not stable, while one more point is asymptotically stable if modified reproduction ratio number more than one and the ratio between intrinsic growth rate with death rate which is caused of disease less than proportion of number of infected person with total population. Based on modified reproduction ratio number, loss of disease from population is affected by the interaction rate between susceptible person with infected person, recovery rate of infected person, death rate which is caused of disease, and birth rate. An endemic equilibrium point is asymptotically stable if basic reproduction ratio number more than one. Based on basic reproduction ratio number, epidemic case in population are affected by several things, they are the interaction rate between susceptible person with infected person, recovery rate of infected person, death rate which is caused of disease, birth rate, the factor which influence birth rate decrease, and intrinsic growth rate.

Pandemic preparedness and new model developments for airborne diseases transmitting via aerosols.

Eigen values and the largest eigen value have special roles in many applications. In this paper we will discuss its role in determining the epidemic threshold in which we can determine if an epidemic will decease or blow out eventually. Some examples and their consequences to controling the epidemic are also discusses. Beside the application in epidemic model, the paper also discusses other example of appication in bio-inspired model, such as the backcross breeding for two age classes of local and exotic goats. Here we give some elaborative examples on the use of previous backcross breeding model. Some future direction on the exploration of the relationship between these eigenvalues to different epidemic models and other bio-inspired models are also presented.

The epidemic growth model is an important tools used in predicting the future of a population and the spread of disease in the population. An epidemic model is usually formed in a differential equation or a system consisting several differential equations. The biological complexity in the underlying population affects the complexity of the epidemic model. One example of biological complexity is the Allee effect which reflects the critical density dependent of the population growth. In this paper we discuss a Logistic epidemic by considering this Allee effect on the population. Dynamic analysis is performed by determining fixed point and its stability analysis in crisp condition. We found the Basic Reproduction Ratio (BRR) for the model. The properties of the solution of the model are explored by the use of its numerical solution. Since we also consider the fuzziness of parameters and variables in the model, the numerical solution is generated using a modified Runge-Kutta method. This is done to explore the effect of inaccuracy and uncertainty which often occur in epidemiological problems.

Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination

An exact global solution for the classical epidemic model

In the 21st century, pre-service mathematics teachers are expected to have problem-solving skills that are effective, efficient, and solutive and are in line with the mindset of computer experts. In learning mathematics, the concept of computational thinking (CT) is also needed and at this time, many still have difficulty solving mathematical problems in general, especially in solving problems in epidemic mathematical models. The subjects of this study were twenty-seven pre-service mathematics teacher students who took mathematical modeling courses. The researcher used the purposive sampling technique to select two research samples. The research method used was a descriptive qualitative research method in exploring the thinking process of pre-service mathematics teacher students in solving the problem of modeling the epidemic spread of disease. The results showed that the thinking process of the first subject began with identifying the problem and existing information by writing down the data in the form of a graph so as to get a certain pattern, which was then used as the basis for the process of transforming the problem into mathematical language. By adding assumptions related to the existence of environmental limitations in the next epidemic model, the concept of differential equations, in which there are integral properties and natural logarithms, can be used to find the solution to the epidemic model. The second subject was unable to solve the integral at hand. The researcher discovered that pre-service mathematics teacher students who correctly solved the problem in the mathematical model used CT components, namely decomposition, abstraction, pattern recognition, algorithm and mathematical literacy.

This paper focuses on transforming a continuous SIR epidemic model into its discrete
counterpart using a non-standard finite difference scheme, motivated by the rich dynamic behaviors often exhibited by discrete models. The study investigates the impact of Allee’s Effect
on disease progression by analyzing the existence of equilibrium points and determining their
stability and bifurcation conditions. Augmenting the model with these factors significantly
enhances our capacity to predict the course of the epidemic. Similarly, assessing the impact
of treatment on epidemic diseases is pivotal for disease control. A thorough understanding of
factors influencing disease dynamics, including Allee’s Effect, is crucial for effective modeling
and prediction of epidemic progression. The transmission rate of the disease fluctuates based
on individual isolation or treatment rates, and incorporating Allee’s Effect adds an extra layer
of complexity to this dynamic. Analyzing mathematical models based on these and similar
factors, including Allee’s Effect, allows us to glean insights into the disease’s trajectory. This
research investigates epidemic disease models that integrate mass action involving treatment,
while also considering the influence of Allee’s Effect. In our investigation, we explore the
existence of equilibrium points and establish the stability and bifurcation conditions of these
points in the context of Allee’s Effect. We complement our analysis with numerical examples.
To compare the behavior of the epidemic disease models under consideration, including those
accounting for Allee’s Effect, we present graphs illustrating the dynamic behaviors of our
populations.

This paper aims to provide a resiliency management strategy of the air transportation network through network stability theory. To ensure the network to recover quickly from an upset condition, an optimization problem has been introduced through network stability upon the meta-population epidemic process model, which is a low-dimensional approximate model of the air traffic flow network. The delay propagation over air traffic network has been modeled as an epidemic spreading process model, which allows to define the whole network through a few states of the individuals (i.e., flights) and recovery rates of the nodes (i.e., airports). The physical parameters of the network extracted from real flight data set are transformed into a parameter set of the epidemic model enabling to simulate the propagation of delay. Moreover, self-organizing maps are used, generating the discretized representation of the input space through an artificial neural network to analyze the European air traffic network with regard to resiliency metrics. Through examples with historical real flight data, it is shown that the applied methodology to control the infection rates, which has the direct projection to operational applications such as ground holding and flight cancellation, effectively enhances the resiliency of the air traffic network under disruptive events.

In this paper, we study a stochastic susceptible-infected-susceptible (SIS) epidemic model that includes an additional immigration process. In the presence of multiplicative noise, generated by environmental perturbations, the model exhibits noise-induced transitions. The bifurcation diagram has two distinct regions of unimodality and bimodality in which the steady-state probability distribution has one and two peaks, respectively. Apart from first-order transitions between the two regimes, a critical-point transition occurs at a cusp point with the transition belonging to the mean-field Ising universality class. The epidemic model shares these features with the well-known Horsthemke-Lefever model of population genetics. The effect of vaccination on the spread/containment of the epidemic in a stochastic setting is also studied. We further propose a general vaccine-hesitancy model, along the lines of Kirman's ant model, with the steady-state distribution of the fraction of the vaccine-willing population given by the Beta distribution. The distribution is shown to give a good fit to the COVID-19 data on vaccine hesitancy and vaccination. We derive the steady-state probability distribution of the basic reproduction number, a key parameter in epidemiology, based on a beta-distributed fraction of the vaccinated population. Our study highlights the universal features that epidemic and vaccine models share with other dynamical models.