We discuss the spread of epidemics caused by two viruses which cannot infect the same individual at the same time. The mathematical modeling of this epidemic leads to a kind of SIIRR model with two groups of infected individuals and two groups of rec...
Based on SEIR (susceptible–exposed–infectious–removed) epidemic model, we propose a modified epidemic mathematical model to describe the spread of the coronavirus disease 2019 (COVID-19) epidemic in Wuhan, China. Using public data,...
Mathematical modeling allows taking into account registered and hidden infections to make correct predictions of epidemic dynamics and develop recommendations that can reduce the negative impact on public health and the economy. A model for visible a...
We develop a mathematical model to provide epidemic predictions for the COVID-19 epidemic in Wuhan, China. We use reported case data up to 31 January 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commi...
Vector-borne diseases pose a significant public health challenge in tropical regions, where complex interactions between hosts, vectors, and the environment drive epidemic dynamics. In this study, we develop a spatio-temporal mathematical model to de...
We investigate the age structured data for the COVID-19 outbreak in Japan. We consider a mathematical model for the epidemic with unreported infectious patient with and without age structure. In particular, we build a new mathematical model and a new...
11 February 2022
The phenomenon of drug epidemics has been a global issue in the past decades, causing enormous damages to the physical and mental health of drug users and social well-being. Despite great efforts to curb drug epidemics at the governmental or social l...
This study investigates a symmetric fractional-order epidemic model with time delays and non-monotonic incidence rates, considering two viral strains. By confirming the existence, uniqueness, and boundedness of the system’s solutions, the resea...
Infectious disease epidemics are challenging for medical and public health practitioners. They require prompt treatment, but it is challenging to recognize and define epidemics in real time. Knowing the prediction of an infectious disease epidemic ca...
The spread of COVID-19 started in late December 2019 and is still ongoing. Many countries around the world have faced an outbreak of COVID-19, including Thailand, which must keep an eye on the spread and find a way to deal with this extreme outbreak....
Owing to the COVID-19 pandemic, which broke out in December 2019 and is still disrupting human life across the world, attention has been recently focused on the study of epidemic mathematical models able to describe the spread of the disease. The num...
This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions...
Stockpiling neuraminidase inhibitors (NAIs) such as oseltamivir and zanamivir is part of a global effort to be prepared for an influenza pandemic. However, the contribution of NAIs for the treatment and prevention of influenza and its complications i...
Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many resear...
After an infectious contact, there is a time lapse before the individual actually becomes infected. In this paper, we present different ways of incorporating this incubation or infection time into epidemic mathematical models. For simplicity, we cons...
Data from the World Health Organization indicate that Bulgaria has the second-highest COVID-19 mortality rate in the world and the lowest vaccination rate in the European Union. In this context, to find the crucial epidemiological parameters that cha...
This paper addresses the problem of describing the spread of COVID-19 by a mathematical model introducing all the possible control actions as prevention (informative campaign, use of masks, social distancing, vaccination) and medication. The model ad...
Lassa fever is a deadly viral illness that is endemic in some parts of West Africa, including Nigeria. A deterministic model in the form of a non-linear system of differential equations is developed to analyse the dynamics and possible control of the...
The full-scale invasion of Ukraine caused an unprecedented number of refugees after 24 February 2022. To estimate the influence of this humanitarian disaster on the COVID-19 pandemic dynamics, the smoothed daily numbers of cases in Ukraine, the UK, P...
This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the inf...
Simple mathematical tools are needed to quantify the threat posed by emerging and re-emerging infectious disease outbreaks using minimal data capturing the outbreak trajectory. Here we use mathematical analysis, simulation and COVID-19 epidemic data...
The regulation policies implemented, the characteristics of vaccines, and the evolution of the virus continue to play a significant role in the progression of the SARS-CoV-2 pandemic. Numerous research articles have proposed using mathematical models...
Most biological processes take time to occur. In infectious diseases, such as malaria or chikungunya, there is a period of time between when a susceptible individual gets bitten by the vector, and when the individual develops the disease. These times...
The results presented in this paper deal with the existence of solutions of a first order fully coupled system of three equations, and they are split in two parts: 1. Case with coupled functional boundary conditions, and 2. Case with periodic boundar...
The integrable versions of SIR epidemic models are introduced. The exact solutions of these models are derived. The advantage of these models is the possibility of full analysis of obtained solutions and the simplicity of explicit formulas for the im...
The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry pro...
The mathematical modeling of infectious diseases plays a vital role in understanding and predicting disease transmission, as underscored by recent global outbreaks; to delve deep into the dynamic of infectious disease considering latent period presci...
The study of contagion dynamics is a well-established domain within epidemiology, where the spread of infectious diseases is modeled and analyzed. In recent years, similar methodologies have been applied to the financial sector to understand and pred...
This paper proposes a mathematical model based on a mechanistic approach and previous research findings for the bacterial canker disease development in kiwifruit vines. This disease is a leading cause of severe damage to kiwifruit vines, particularly...
In this paper, we analyzed and found the solution for a suitable nonlinear fractional dynamical system that describes coronavirus (2019-nCoV) using a novel computational method. A compartmental model with four compartments, namely, susceptible, infec...
In this paper, we study and present a mathematical modeling approach based on artificial neural networks to forecast the number of cases of respiratory syncytial virus (RSV). The number of RSV-positive cases in most of the countries around the world...
We describe results from a panel study in which pigs from a 17-sow African swine fever (ASF) positive herd in Thái Bình province, Vietnam, were followed over time to record the date of onset of ASF signs and the date of death from ASF....
Monkeypox (mpox) is a zoonotic viral disease that has caused recurring outbreaks in West Africa. The current global mpox virus (mpoxv) epidemic in endemic and non-endemic areas has seriously threatened public health. In this study, we design an SEIR-...
We use a new modelling approach to predict the cumulative impact of Phytophthora ramorum on the dynamic distribution of tanoak (Notholithocarpus densiflorus) and other tree species in coastal-Californian forest-communities. We explore the effectivene...
22 March 2018
Elevating herd immunity level against rubella is essential to prevent congenital rubella syndrome (CRS). Insufficient vaccination coverage left susceptible pockets among adults in Japan, and the outbreak of rubella from 2012 to 2013 resulted in 45 ob...
In this paper, we propose a novel normalized time-fractional susceptible–infected–removed (SIR) model that incorporates memory effects into epidemiological dynamics. The proposed model is based on a newly developed normalized time-fractio...
A spatiotemporal transmission epidemic model is proposed based on human mobility, spatial factors of population migration across multiple regions, individual protection, and government quarantine measures. First, the model’s basic reproduction...
26 May 2021
Heterogeneities of individual attributes and behaviors play an important role in the complex process of epidemic spreading. Compared to differential equation-based system dynamical models of infectious disease transmission, individual-based epidemic...
The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-1...
We developed a mathematical model to study the effects of non-pharmaceutical interventions (NPIs) on the dynamics of an epidemic. The level of intervention was assessed as a fraction of the population being isolated and depended on the level of incid...
Based on China’s summary of three years of experience and measures in the prevention and control of the COVID-19 epidemic, we have built a COVID-19 prevention and control model integrating health and medical detection, big data information tech...
An HFMD outbreak spread over the city of Hải Phòng from summer 2011 to autumn 2012. This epidemic was chosen because it was the very first HFMD epidemic in North Vietnam, eliminating thus interferences with previous outbreaks. This epide...
The calculation of the probability of a minor outbreak is crucial in analyzing a stochastic epidemic model. For stochastic epidemic models with fixed delays, the linear chain trick is applied to transform the delayed models into a family of ODE model...
A local performance of the SIR model on actual data is introduced. A good approximation of the SIR model parameters in Saudi Arabia during a period of 275 days (the first of April 2020 to the end of December 2020) is determined. The parameters are es...
We consider a mosquito-borne epidemic model, where the adoption by individuals of insecticide–treated bed–nets (ITNs) is taken into account. Motivated by the well documented strong influence of behavioral factors in ITNs usage, we propose a mathemati...
Mathematical modeling in epidemiology, biology, and life sciences requires the use of stochastic models. In this paper, we derive a competitive two-strain stochastic SIR epidemic model by considering the change in state of the epidemic process due to...
The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that inc...
The COVID-19 pandemic has had a significant impact on countries worldwide, including the United Kingdom (UK). The UK has faced numerous challenges, but its response, including the rapid vaccination campaign, has been noteworthy. While progress has be...
Mathematical models of the spread of epidemic diseases are studied, paying special attention to networks. We treat the Susceptible-Infected-Recovered (SIR) model and the Susceptible-Exposed-Infectious-Recovered (SEIR) model described by differential...
The susceptible–infected–recovered–vaccinated–deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encomp...
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