Mathematical modelling of the first HIV/ZIKV co-infection cases in Colombia and Brazil

This paper presents a mathematical model to investigate co-infection with HIV/AIDS and zika virus (ZIKV) in Colombia and Brazil, where the first cases were reported in 2015-2016. The model considers the sexual transmission dynamics of both viruses and vector-host interactions. We begin by exploring the qualitative behaviour of each model separately. Then, we analyze the dynamics of the co-infection model using the thresholds and results defined separately for each model. The model also considers the impact of intervention strategies, such as, personal protection, antiretroviral therapy (ART), and sexual protection (condoms use). Using available parameter values for Colombia and Brazil, the model is calibrated to predict the potential effect of implementing combinations of those intervention strategies on the co-infection spread. According to these findings, transmission through sexual contact is a determining factor in the long-term behaviour of these two diseases. Furthermore, it is important to note that co-infection with HIV and ZIKV may result in higher rates of HIV transmission and an increased risk of severe congenital disabilities linked to ZIKV infection. As a result, control measures have been implemented to limit the number of infected individuals and mosquitoes, with the aim of halting disease transmission. This study provides novel insights into the dynamics of HIV/ZIKV co-infection and highlights the importance of integrated intervention strategies in controlling the spread of these viruses, which may impact public healt

A Discrete, Size-Structured Model of Phytoplankton Growth in The Chemostat

We introduce inhomogeneous, substrate dependent cell division in a nonlinear matrix model of size-structured population growth in the chemostat, first introduced by Gage et al. [7] and later analyzed by Smith [11]. We show that mass conservation is verified, and conclude that our system admits one non zero globally stable equilibrium, which we express explicitly. We then proceed to several numerical simulations, and briefly compare the prediction of the model to data, whose obtention we discuss

Antiviral resistance during pandemic influenza: implications for stockpiling and drug use

<p>Abstract</p> <p>Background</p> <p>The anticipated extent of antiviral use during an influenza pandemic can have adverse consequences for the development of drug resistance and rationing of limited stockpiles. The strategic use of drugs is therefore a major public health concern in planning for effective pandemic responses.</p> <p>Methods</p> <p>We employed a mathematical model that includes both sensitive and resistant strains of a virus with pandemic potential, and applies antiviral drugs for treatment of clinical infections. Using estimated parameters in the published literature, the model was simulated for various sizes of stockpiles to evaluate the outcome of different antiviral strategies.</p> <p>Results</p> <p>We demonstrated that the emergence of highly transmissible resistant strains has no significant impact on the use of available stockpiles if treatment is maintained at low levels or the reproduction number of the sensitive strain is sufficiently high. However, moderate to high treatment levels can result in a more rapid depletion of stockpiles, leading to run-out, by promoting wide-spread drug resistance. We applied an antiviral strategy that delays the onset of aggressive treatment for a certain amount of time after the onset of the outbreak. Our results show that if high treatment levels are enforced too early during the outbreak, a second wave of infections can potentially occur with a substantially larger magnitude. However, a timely implementation of wide-scale treatment can prevent resistance spread in the population, and minimize the final size of the pandemic.</p> <p>Conclusion</p> <p>Our results reveal that conservative treatment levels during the early stages of the outbreak, followed by a timely increase in the scale of drug-use, will offer an effective strategy to manage drug resistance in the population and avoid run-out. For a 1918-like strain, the findings suggest that pandemic plans should consider stockpiling antiviral drugs to cover at least 20% of the population.</p

Modélisation structurée de la croissance du phytoplancton en chemostat

Jury: François Houllier (Président), Michel Langlais (Rapporteur), Hal L. Smith (Rapporteur), Pierre Baconnier (Examinateur), Jean-Luc Gouzé (Examinateur), Antoine Sciandra (Examinateur).This thesis deals with the formulation and analysis of structured models of growth in a chemostat, an experimental device used for the culture of micro-organisms in idealized conditions. More specifically, we will be concerned with the description of the size of phytoplanktonic organisms. In a first part, we give some biological indications concerning phytoplankton, then describe the experimental apparatus and finally introduce the mathematical models used for an elementary description of the chemostat. The second and main part of this thesis begins by an introduction to structured population models, with emphasis on cellular division description. Then time discrete models describing in a detailed way cellular division are studied, followed by ordinary differential equations systems verifying the mass conservation principle, and finally by a class of models that do not verify this property. We end this thesis by considering possible applications to other contexts or populations of the type of models developped herein.L'objet de cette thèse est la formulation et l'étude de modèles structurés de croissance dans un chemostat, qui est un appareil permettant la culture de micro-organismes dans des conditions très contrôlées. Plus particulièrement, nous serons intéressés par la description de la taille d'organismes phytoplanctoniques. Dans une première partie, nous donnons quelques précisions biologiques, présentons ensuite le dispositif expérimental, puis introduisons les modèles élémentaires utilisés pour la description mathématique du chemostat. La deuxième et principale partie de cette thèse commence par une introduction aux modèles structurés de populations, l'accent étant mis sur la description des populations cellulaires. Ensuite sont étudiés successivement des modèles discrets en temps détaillant de manière précise la division cellulaire, des modèles en équations différentielles ordinaires vérifiant la propriété dite de conservation de la matière, et enfin une classe de modèles ne vérifiant pas cette propriété. Nous terminons cette thèse par une ouverture sur les possibles applications à d'autres contextes du type de modélisation que nous développons

Spatio-temporal spread of infectious pathogens of humans

Spatio-temporal aspects in the propagation of infectious pathogens of humans are reviewed. Mathematical modelling of these issues using metapopulation models is presented