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This paper gives an introduction to rule-based modelling applied to topics in infectious diseases. Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in…
A four dimensional ecoepidemiological model consisting of susceptible prey, infected prey, vaccinated prey and predator is formulated and analyzed in the present work. The functional response is assumed to be of Lotka-Volterra type. We…
Epidemic models study the spread of an undesired agent through a population, be it infectious diseases through a country, misinformation in online social media, or pests infesting a region. In combating these epidemics, we rely neither on…
Epidemiological models are an important tool in coping with epidemics, as they offer a forecast, even if often simplistic, of the behavior of the disease in the population. This allows responsible health agencies to organize themselves and…
A problem closely related to epidemiology, where a subgraph of 'infected' links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…
Arboviruses represent a significant threat to human, animal, and plant health worldwide. To elucidate transmission, anticipate their spread and efficiently control them, mechanistic modelling has proven its usefulness. However, most models…
A model capturing the dynamics between virus and tumour cells in the context of oncolytic virotherapy is presented and analysed. The ability of the virus to be internalised by uninfected cells is described by an infectivity parameter, which…
This review presents and reviews various solved and open problems in developing, analyzing, and mitigating epidemic spreading processes under human decision-making. We provide a review of a range of epidemic models and explain the pros and…
It is essential to understand the dynamics of epidemics in the presence of coexisting pathogens. There are various phenomenon that can effect the dynamics. In this paper, we formulate a mathematical model using different assumptions to…
Epidemics exhibit interconnected processes that operate at multiple time and organizational scales, a hallmark of complex adaptive systems. Modern epidemiological modeling frameworks incorporate feedback between individual-level behavioral…
Insect-borne diseases are diseases carried by insects affecting humans, animals or plants. They have the potential to generate massive outbreaks such as the Zika epidemic in 2015-2016 mostly distributed in the Americas, the Pacific and…
Is it possible to break the host-vector chain of transmission when there is an influx of infectious hosts into a na\"{i}ve population and competent vector? To address this question, a class of vector-borne disease models with an arbitrary…
Epidemic spread in single-host systems strongly depends on the population's contact network. However, little is known regarding the spread of epidemics across networks representing populations of multiple hosts. We explored cross-species…
Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected…
We consider an epidemiological model that includes waning and boosting of immunity. Assuming that repeated exposure to the pathogen fully restores immunity, we derive an SIRS-type model with discrete and distributed delays. First we prove…
Motivated by recent outbreaks of the Ebola Virus, we are concerned with the role that a vector reservoir plays in supporting the spatio-temporal spread of a highly lethal disease through a host population. In our context, the reservoir is a…
A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The…
Human mobility, contact patterns, and their interplay are key aspects of our social behavior that shape the spread of infectious diseases across different regions. In the light of new evidence and data sets about these two elements,…