Related papers: Analysis of a Stochastic Predator-Prey Model with …
Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune response against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the percentage of immunogenic cells (i.e.…
The positivity assumption is central in the identification of a causal effect, and especially the stochastic variant is an issue many applied researchers face, yet is rarely discussed, especially in conjunction with continuous treatments or…
We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
In this paper, we investigate a novel 3-compartment model of HIV infection of CD4$^+$ T-cells with a mass action term by including two versions: one baseline ODE model and one delay-differential equation (DDE) model with a constant discrete…
Between-species coevolution, and in particular antagonistic host-parasite coevolution, is a major process shaping within-species diversity. In this paper we investigate the role of various stochastic processes affecting the outcome of the…
HIV pre-exposure prophylaxis (PrEP) drastically reduces the risk of HIV infection if taken as prescribed, providing almost perfect protection even during unprotected sexual intercourse. Although this has been transformative in reducing new…
We propose and investigate a delayed model that studies the relationship between HIV and the immune system during the natural course of infection and in the context of antiviral treatment regimes. Sufficient criteria for local asymptotic…
RNA viruses are a widely used tool to study evolution experimentally. Many standard protocols of virus propagation and competition are done at nominally low multiplicity of infection (m.o.i.), but lead during one passage to two or more…
The precise mechanism that causes HIV infection to progress to AIDS is still unknown. This paper presents a mathematical model which is able to predict the entire trajectory of the HIV/AIDS dynamics, then a possible explanation for this…
A host-parasite model is considered for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a B-cell always splits into two cells of the same type, the two daughter cells of an A-cell can be…
When highly active antiretroviral therapy is administered for long periods of time to HIV-1 infected patients, most patients achieve viral loads that are ``undetectable'' by standard assay (i.e., HIV-1 RNA $ < 50$ copies/ml). Yet despite…
We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types that can mutate into each other in a common host population. Instead of using a single virulence…
Inspired by DNA data of the human cytomegalovirus we propose a model of a two-type parasite population distributed over its hosts. The parasite is capable to persist in its host till the host dies, and to reinfect other hosts. To maintain…
Honest signals and cues have been observed as part of interspecific and intraspecific communication among animals. Recent theories suggest that existing signaling systems have evolved through natural selection imposed by predators. Honest…
Tumor-immune interactions are shaped by both antigenic heterogeneity and stochastic perturbations in the tumor microenvironment, yet the mathematical mechanisms underlying immune phase transitions remain poorly understood. We propose a…
In this paper, we study the stochastic optimal control problem for the PReP vaccine in the stochastic model for HIV/AIDS with PReP. By using the stochastic maximum principle, we derive the stochastic optimal control of PReP for the…
HIV transmission within serodiscordant couples remains a significant public health challenge, particularly in sub-Saharan Africa. Estimating the rate of such infection, alongside the rates of introduction of infection from outside the…
To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessions were regular, a…
We consider a general mathematical model of a within-host viral infection with $n$ virus strains and explicit age-since-infection structure for infected cells. In the model, multiple virus strains compete for a population of target cells.…