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Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics,…
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…
When an infectious disease propagates throughout society, the incidence function may rise at first due to an increase in pathogenicity and then decrease due to inhibitory effects until it reaches saturation. Effective vaccination and…
During an epidemic, infectious individuals might not be detectable until some time after becoming infected. The studies show that carriers with mild or no symptoms are the main contributors to the transmission of a virus within the…
Diagnostic testing followed by isolation of identified cases with subsequent tracing and quarantine of close contacts - often referred to as test-trace-isolate-and-quarantine (TTIQ) strategy - is one of the cornerstone measures of…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
In this paper, we consider the impact of time delay by media on the control of the disease. We set up a class of SISM epidemic model with the time delay and the cumulative density of awareness caused by media. The sufficient condition of…
Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts…
The spontaneous behavioral changes of the agents during an epidemic can have significant effects on the delay and the prevalence of its spread. In this work, we study a social distancing game among the agents of a population, who determine…
The spread of infectious diseases crucially depends on the pattern of contacts among individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. Few empirical studies are however available that…
Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails…
One of the most significant challenges in combating against the spread of infectious diseases was the difficulty in estimating the true magnitude of infections. Unreported infections could drive up disease spread, making it very hard to…
The effect of public health interventions on an epidemic are often estimated by adding the intervention to epidemic models. During the Covid-19 epidemic, numerous papers used such methods for making scenario predictions. The majority of…
Epidemic spreading of infectious diseases is ubiquitous and has often considerable impact on public health and economic wealth. The large variability in spatio-temporal patterns of epidemics prohibits simple interventions and demands for a…
Two crucial elements facilitate the understanding and control of communicable disease spread within a social setting. These components are, the underlying contact structure among individuals that determines the pattern of disease…
Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious…
Diseases and other contagion phenomena in nature and society can interact asymmetrically, such that one can benefit from the other, which in turn impairs the first, in analogy with predator-prey systems. Here, we consider two models for…
The accurate estimation of time-varying transmission rates is fundamental for understanding infectious disease dynamics and implementing effective public health interventions. To this end, we propose an improved inverse method for…
The isolation of infectious individuals is a key measure of public health for the control of communicable diseases. However, involving a strong perturbation of daily life, it often causes psychosocial distress, and severe financial and…