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Different countries -- and sometimes different regions within the same countries -- have adopted different strategies in trying to contain the ongoing COVID-19 epidemic; these mix in variable parts social confinement, early detection and…
The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The…
In this study, we develop the mathematical model to understand the coupling between the spreading dynamics of infectious diseases and the mobility dynamics through urban transportation systems. We first describe the mobility dynamics of the…
A pulse vaccination SIR model with periodic infection rate $\beta (t)$ have been proposed and studied. The basic reproductive number $R_0$ is defined. The dynamical behaviors of the model are analyzed with the help of persistence,…
Human behavior plays a critical role in shaping epidemic trajectories. During health crises, people respond in diverse ways in terms of self-protection and adherence to recommended measures, largely reflecting differences in how individuals…
We are currently facing a highly critical case of a world-wide pandemic. The novel coronavirus (SARS-CoV-2, a.k.a. COVID-19) has proved to be extremely contagious and the original outbreak from Asia has now spread to all continents. This…
In contrast to the many theoretical studies on the transmission of human-mosquitoes malaria infection, few studies have considered a multiple structure model formulations including (i) the chronological age of humans and mosquitoes…
In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while…
Since December 2019, A novel coronavirus (2019-nCoV) has been breaking out in China, which can cause respiratory diseases and severe pneumonia. Mathematical and empirical models relying on the epidemic situation scale for forecasting…
Ebola virus is one of the most virulent pathogens for humans. We present a mathematical description of different Susceptible-Exposed-Infectious-Recovered (SEIR) models. By using mathematical modeling and analysis, the latest major outbreak…
Many infectious diseases can lead to re-infection. We examined the relationship between the prevalence of repeat infection and the basic reproductive number (R0). First we solved a generic, deterministic compartmental model of re-infection…
An SIR epidemic model with free boundary is investigated. This model describes the transmission of diseases. The behavior of positive solutions to a reaction-diffusion system in a radially symmetric domain is investigated. The existence and…
I employ a simple mathematical model of an epidemic process to evaluate how four basic quantities: the reproduction number (R), the numbers of sensitive (S) and infectious individuals(I), and total community size (N) affect strategies to…
Rabies remains a pressing global public health issue, demanding effective modeling and control strategies. This study focused on developing a mathematical model using ordinary differential equations (ODEs) to estimate parameters and assess…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and…
We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…
SIR models, also with age structure, can be used to describe the evolution of an infective disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered…
This paper analyses an SIRS-type model for infectious diseases with account for behavioural changes associated with the simultaneous spread of awareness in the population. Two types of awareness are included into the model: private…
Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields ele…