The two most common ways to prevent spreading drug addiction are counseling and imprisonment. In this paper, we propose and study a model for the spread of drug addiction incorporating the effect of consultation and incarceration of addicted individuals. We extract the basic reproductive ratio and study the occurrence of backward bifurcation. Also, we study the local and global stability of drug-free and endemic equilibria under suitable conditions. Finally, we use numerical simulations to illustrate the obtained analytical results.

Background: In recent years, there has been an increase in the amount and variety of data generated in the field of healthcare, (e.g., data related to the prevalence of contagious diseases in the society). Various patterns of individuals’ relationships in the society make the analysis of the network a complex, highly important process in detecting and preventing the incidence of diseases. Therefore, it would be helpful to propose a model for storing and processing related data which is especially designed for such an application.Materials and Methods: In this paper, a data model is proposed for the management of data for individuals infected with contagious diseases. This data model has the ability to efficiently detect the path of infectious diseases and the probable Epidemicity. The proposed model is based on the graph data model, a type of NoSQL data model. In order to design this data model, essential requirements and queries were determined based on the needs of experts in this field.Results: The proposed data model was experimentally evaluated using Neo4j, a well-known graph data management system. It is shown in this paper that the proposed data model has a better performance than the traditional relational model in terms of system utilization and performance (i.e., data storage space, complexity and the time of finding the shortest infection path between two individuals, traversing the graph, finding at risk individuals, and etc.).Conclusions: The management of data for Epidemic detection of HIV infection requires an appropriate data model that can provide the required functionalities and features with an acceptable quality. Graph data models are suitable NoSQL models for some of these features (e.g., Epidemic detection via traversing of the graph). The proposed graph-based data model provides the main functionalities and features while outperforming performance and utilization metrics.

We consider a mathematical model of Epidemic spread in which the population is partitioned into five compartments of susceptible S (t), Infected I (t), Removed R (t), Pre- vented U (t) and the Controlled W (t). We assume each of the compartments comprises of cohorts of individuals which are identical with respect to the disease status. We derive five systems of equations to represent each of the subpopulations. The general stability of the disease free equilibrium (DFE) and the endemic equilibrium states of the linearized model are established using the linear stability theory and the Routh-Hurwitz conditions are established and analyzed in the domain of interest. We find that the DFE is locally asymptotically stable when the infected individuals received ART and use the condom but the endemic state is unstable to initial perturbations. Also, we derive an expression for the basic reproduction number using the next generation matrix approach and find that for R0<1 the DFE is stable but for R0>1 is unstable.

In this paper, we consider a mathematical model of leptospirosis disease which is an infectious disease. The model we are considering is a system of nonlinear ordinary differential equations and it is difficult to find exact solution. He’ s homotopy perturbation method is employed to compute an approximation to the solution of the system of nonlinear ordinary differential equations governing on the problem. The findings obtained by HPM are compared with nonstandard finite difference (NSFD) and Runge-Kutta fourth order (RK4) methods. Some plots are presented to show the reliability and simplicity of the method.

In this paper, an Epidemic model with fuzzy parameters for spreading COVID-19 in a population is considered. The sensitivity analysis is used to determine the model robustness to parameter values of the model. The basic reproduction number of the Epidemic model denoted by R_0 determines the dynamics of the model. Then, in order to examine the relative importance of different parameters in the COVID-19 spread, we derive an analytical expression for the sensitivity of the basic reproduction number R_0, namely sensitivity index, with respect to each parameter involved in the model. Finally,  sensitivity analysis results and the numerical simulations of the model are given with different parameter values.

In this work, we analyse a pair of two-dimensional coupled reaction-diffusion equations known as the Gray-Scott model, in which spot patterns have been observed. We focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. A complete numerical study of the system is presented. We use backward Euler and Crank-Nicolson methods to study the model 1. We compute the error in L2 and L ¥ norms and also the EOCS are calculated for each method. The errors and the EOCs show that the methods converge with the correct order.The main mathematical techniques employed in this analysis of the stationary patterns is the Turing instability theory. This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the Gray-Scott model by Turing mechanisms.In particular, we present a theoretical analysis of results of the numerical simulations in two dimensions. We have observed the formation of spatial patterns during the evolution, which are sparsely isolated ordered spot patterns that emerge in space. In this research we focuse on three areas: first, the analytical analysis; second, the numerical analysis and third, the application. We use these spatial patterns to understand the nature of population distribution and to understand the mechanism of interaction of the populations.

Background: The Coronavirus 2019-nCOV (COVID-19) Epidemic by SARS-CoV-2 is spreading worldwide, and by March 1, 2020, 67 countries, including Iran, have been affected. Many studies are being conducted at home and abroad to predict the outbreak of the disease so that they can make the necessary medical and health decisions in a timely manner. Methods: we used the SIR model to identify parameters to calculate Epidemic features and some estimates of the new coronavirus. Data on the transmission of the novel coronavirus were extracted from the GitHub source in the covid19. analytics software package. Results: According to our model estimates, the rate of infection β = 1 and the rate of removal γ = 0. 667 and index R0 = 1. 497 were obtained. Because the value of R0 is more than one, it is still an Epidemic disease. Given that tfinal~132 days was estimated, we can expect the transmission of this Epidemic to stop in Iran after July 3, 2020, provided that existing quarantine measures and patient isolation rates continue as usual. In comparison with the global SIR model, we reached the peak of the infection earlier than the global model, but in improved and susceptible cases, we performed better than the global model. The graph of recovered and susceptible cases in Iran earlier than the global model cut off themselves. Conclusion: Forecasts are set to be a useful guide for deciding whether to transfer COVID-19. According to the predictions and estimates made, more attention should be paid to control measures.