Related papers: Backward bifurcation in SIRS malaria model
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…
An SIRS type model of disease transmission in an open environment is discussed. We use the Poincar\'{e} index together with a perturbation method to show that the endemic proportions need not be unique.
Although viral spreading processes taking place in networks are often analyzed using Markovian models in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real…
In this paper, we consider the dynamics of a delayed reaction-diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary…
Epidemics have shaped human history, often with devastating consequences, motivating the development of mathematical models to understand and control their dynamics. Among the many aspects of epidemic behavior, the conditions that lead to…
Studies in malaria control cover many areas such as medicine, sociology, biology, mathematic, physic, computer science and so forth. Researches in the realm of mathematic are conducted to predict the occurrence of the disease and to support…
In this paper, the dynamics of a phytoplankton-zooplankton system with linear functional responses are examined. For the continuous-time model, the global asymptotic stability of the fixed points is demonstrated by constructing Lyapunov…
Malaria, a mosquito-borne disease caused by a parasite, kills over 1 million people globally each year. People, if left untreated, may develop severe complications, leading to death. Effective and accurate diagnosis is important for the…
We use scale-free networks to study properties of the infected mass $M$ of the network during a spreading process as a function of the infection probability $q$ and the structural scaling exponent $\gamma$. We use the standard SIR model and…
The state of the art of epidemic modelling in terrestrial ecosystems is the compartmental SIR model and its extensions from the now classical work of Kermack-Mackendrick. In contrast, epidemic modelling of marine ecosystems is a bit behind,…
Treatment rate has always been one of the most important factors affecting the spread of infectious diseases. In this paper, we study a treatment function SIR model with treatment rate related to the maximum treatment capacity, whose…
In this paper we introduce the functional framework and the necessary conditions for the well-posedness of an inverse problem arising in the mathematical modeling of disease transmission. The direct problem is given by an initial boundary…
According to the World Malaria Report of 2022, 247 million cases of malaria and 619,000 related deaths were reported in 2021. This highlights the predominance of the disease, especially in the tropical and sub-tropical regions of Africa,…
In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the…
We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence…
Recent statistics of malaria shows that over 200 million cases and estimated deaths of nearly half a million occur globally. Africa alone accounts for almost 90% of the cases. Several studies have been conducted to understand the disease…
Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence…
In this paper, we consider a 3-dimensional free boundary problem modeling tumor growth with the Robin boundary condition. The system involves a positive parameter $\mu$ which reflects the intensity of tumor aggressiveness. Huang, Zhang and…
Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses…
We show the existence of traveling front solutions in a diffusive classical SIS epidemic model and the SIS model with a saturating incidence in the size of the susceptible population. We investigate the situation where both susceptible and…