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Wolbachia infection in Anopheles albimanus mosquitoes can render mosquitoes less capable of spreading malaria. We develop and analyze an ordinary differential equation model to evaluate the effectiveness of Wolbachia-based vector control…

We explore the role of cellular life cycles for viruses and host cells in an infection process. For this purpose, we derive a generalized version of the basic model of virus dynamics (Nowak, M.A., Bangham, C.R.M., 1996. Population dynamics…

In this paper, we propose a simplified bidimensional Wolbachia infestation model in a population of Aedes aegypti mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional…

This article proposes an age-structured compartment model for irreversible diseases with a pre-clinical state of undiagnosed cases that precedes the diagnosis. The model is able to cope with mortality rates differing between the…

We study the biological situation when an invading population propagates and replaces an existing population with different characteristics. For instance, this may occur in the presence of a vertically transmitted infection causing a…

We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the…

In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…

Scientists have been seeking ways to use Wolbachia to eliminate the mosquitoes that spread human diseases. Could Wolbachia be the determining factor in controlling the mosquito-borne infectious diseases? To answer this question…

Artificial releases of Wolbachia-infected Aedes mosquitoes have been under study in the past years for fighting vector-borne diseases such as dengue, chikungunya and zika. Several strains of this bacterium cause cytoplasmic incompatibility…

Myxobacteria are social bacteria, that can glide in 2D and form counter-propagating, interacting waves. Here we present a novel age-structured, continuous macroscopic model for the movement of myxobacteria. The derivation is based on…

In this manuscript we consider an age structured epidemic system modelling the dynamics of transmission of immunizing disease like Hepatitis B virus. Our model takes into account age as well as two classes of infected individuals (chronic…

Symbiotic interactions between microbes and their multicellular hosts have manifold impacts on molecular, cellular and organismal biology. To identify candidate bacterial genes involved in maintaining endosymbiotic associations with insect…

We consider an age-structured epidemic model with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and quarantine of the contacts of identified infectives. The dynamics of the infected…

Some viruses, such as human immunodeficiency virus, can infect several types of cell populations. The age of infection can also affect the dynamics of infected cells and production of viral particles. In this work, we study a virus model…

A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for the same purposes. The Lie symmetry classification of the…

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of…

We investigate an infection-age structured competitive epidemiological model involving multiple strains. While classical results establish competitive exclusion when a unique maximal basic reproduction number exists, we provide here a…

Bacteriophages are viruses infecting bacteria and archaea. Many phage species cause infections which lead to the certain death of the infected prokaryotic host cell and the release of a large batch of phage progeny, yet they have been able…

Malaria is one of the most common mosquito-borne diseases widespread in tropical and subtropical regions, causing thousands of deaths every year in the world. In a previous paper, we formulated an age-structured model containing three…

In this paper we analyze a continuous-time epidemic model and its discrete counterpart, where infection spreads both horizontally and vertically. We consider three cases: model with horizontal and imperfect vertical transmissions, model…