Linked within-host and between-host models and data for infectious diseases: a systematic review

The observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: within-host, that is, how an infection progresses inside a single individual (for instance viral and immune dynamics), and between-host, that is, how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a holistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission (as defined by combining within-host and between-host scales) to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 24 of 197 qualifying papers across 30 years that include both linked models at the within and between host scales and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction

The Role of Vector Trait Variation in Vector-Borne Disease Dynamics

Many important endemic and emerging diseases are transmitted by vectors that are biting arthropods. The functional traits of vectors can affect pathogen transmission rates directly and also through their effect on vector population dynamics. Increasing empirical evidence shows that vector traits vary significantly across individuals, populations, and environmental conditions, and at time scales relevant to disease transmission dynamics. Here, we review empirical evidence for variation in vector traits and how this trait variation is currently incorporated into mathematical models of vector-borne disease transmission. We argue that mechanistically incorporating trait variation into these models, by explicitly capturing its effects on vector fitness and abundance, can improve the reliability of their predictions in a changing world. We provide a conceptual framework for incorporating trait variation into vector-borne disease transmission models, and highlight key empirical and theoretical challenges. This framework provides a means to conceptualize how traits can be incorporated in vector borne disease systems, and identifies key areas in which trait variation can be explored. Determining when and to what extent it is important to incorporate trait variation into vector borne disease models remains an important, outstanding question

Prediction and Optimal Scheduling of Advertisements in Linear Television

Advertising is a crucial component of marketing and an important way for companies to raise awareness of goods and services in the marketplace. Advertising campaigns are designed to convey a marketing image or message to an audience of potential consumers and television commercials can be an effective way of transmitting these messages to a large audience. In order to meet the requirements for a typical advertising order, television content providers must provide advertisers with a predetermined number of impressions in the target demographic. However, because the number of impressions for a given program is not known a priori and because there are a limited number of time slots available for commercials, scheduling advertisements efficiently can be a challenging computational problem. In this case study, we compare a variety of methods for estimating future viewership patterns in a target demographic from past data. We also present a method for using those predictions to generate an optimal advertising schedule that satisfies campaign requirements while maximizing advertising revenue

Prediction and Optimal Scheduling of Advertisements in Linear Television

Advertising is a crucial component of marketing and an important way for companies to raise awareness of goods and services in the marketplace. Advertising campaigns are designed to convey a marketing image or message to an audience of potential consumers and television commercials can be an effective way of transmitting these messages to a large audience. In order to meet the requirements for a typical advertising order, television content providers must provide advertisers with a predetermined number of impressions in the target demographic. However, because the number of impressions for a given program is not known a priori and because there are a limited number of time slots available for commercials, scheduling advertisements efficiently can be a challenging computational problem. In this case study, we compare a variety of methods for estimating future viewership patterns in a target demographic from past data. We also present a method for using those predictions to generate an optimal advertising schedule that satisfies campaign requirements while maximizing advertising revenue

Mathematical modelling of bacterial attachment to surfaces : biofilm initiation

Thesis (MSc)--Stellenbosch University, 2011.ENGLISH ABSTRACT: Biofilms are aggregations of bacteria that can thrive wherever there is a watersurface or water-interface. Sometimes they can be beneficial; for example, biofilms are used in water and waste-water treatment. The filter used to remove contaminants acts as a scaffold for microbial attachment and growth. However, biofilms could have bad effects, especially on a persons health. They can cause chronic diseases and serious infections. The importance of biofilms in industrial and medical settings, is the main reason of the mathematical studies performed up to now, concerning biofilms. Biofilms have been mathematical modelling targets over the last 30 years. The complex structure and growth of biofilms make them difficult to study. Biofilm formation is a multi-stage process and occurs in even the most unlikely of environmental conditions. Models of biofilms vary from the discrete to the continuous; accounting for one-species to multi-species and from one-scale to multi-scale models. A model may even have both discrete and continuous parts. The implication of these differences is that the tools used to model biofilms differ; we present and review some of these models. The aim in this thesis is to model the early initiation of biofilm formation. This stage involves bacterial movement towards a surface and the attachment to the boundary which seeds a biofilm. We use a diffusion equation to describe a bacterial random walk and appropriate boundary conditions to model surface attachment. An analytical solution is obtained which gives the bacterial density as a function of position and time. The model is also analysed for stability. Independent of this model, we also give a reaction diffusion equation for the distribution of sensing molecules, accounting for production by the bacteria and natural degradation. The last model we present is of Keller-Segel type, which couples the dynamics of bacterial movement to that of the sensing molecules. In this case, bacteria perform a biased random walk towards the sensing molecules. The most important part of this chapter is the derivation of the boundary conditions. The adhesion of bacteria to a surface is presented by zero-Dirichlet boundary conditions, while the equation describing sensing molecules at the interface needed particular conditions to be set. Bacteria at the boundary also produce sensing molecules, which may then diffuse and degrade. In order to obtain an equation that includes all these features we assumed that mass is conserved. We conclude with a numerical simulation.AFRIKAANSE OPSOMMING: Biofilms is die samedromming van bakterieë wat kan floreer waar daar ’n wateroppervlakte of watertussenvlak is. Soms kan hulle voordelig wees, soos byvoorbeeld, biofilms word gebruik in water en afvalwater behandeling. Die filter wat gebruik word om smetstowwe te verwyder, dien as ’n steier vir mikrobiese verbinding en groei. Biofilms kan ook egter slegte gevolge he, veral op ’n persoon se gesondheid. Hulle kan slepende siektes en ernstige infeksies veroorsaak. Die belangrikheid van biofilms in industriële en mediese omgewings, is die hoof rede vir die wiskundige studies wat tot dusver uitgevoer is met betrekking tot biofilms. Biofilms is oor die afgelope 30 jaar al ’n teiken vir wiskundige modellering. Die komplekse struktuur en groei van biofilms maak dit moeilik om hul te bestudeer. Biofilm formasie is ’n multi-fase proses, en gebeur selfs in die mees onwaarskynlikste omgewings. Modelle wat biofilms beskryf wissel van die diskreet tot die kontinu, inkorporeer een of meer spesies, en strek van eentot multi-skaal modelle. ’n Model kan ook oor beide diskreet en kontinue komponente besit. Dit beteken dat die tegnieke wat gebruik word om biofilms te modelleer ook verskil. In hierdie proefskrif verskaf ons ’n oorsig van sommige van hierdie modelle. Die doel in hierdie proefskrif is om die vroeë aanvang van biofilm ontwikkeling te modeleer. Hierdie fase behels ’n bakteriële beweging na ’n oppervlak toe en die aanvanklike aanhegsel wat sal ontkiem in ’n biofilm. Ons gebruik ’n diffusievergelyking om ’n bakteriële kanslopie te beskryf, met geskikte randvoorwaardes. ’n Analities oplossing is verkry wat die bakteriële bevolkingsdigtheid beskryf as ’n funksie van tyd en posisie. Die model is ook onleed om te toets vir stabiliteit. Onafhanklik van die model, gee ons ook ’n reaksiediffusievergelyking vir die beweging van waarnemings-molekules, wat insluit produksie deur die bakterieë en natuurlike afbreking. Die laaste model wat ten toon gestel word is ’n Keller-Segel tipe model, wat die bakteriese en waarnemings-molekule dinamika koppel. In hierdie geval, neem die bakterieë ’n sydige kanslopie agter die waarnemings molekules aan. Die belangrikste deel van hierdie hoofstuk is die afleiding van die randvoorwaardes. Die klewerigheid van die bakterieë tot die oppervlak word vvorgestel deur nul-Dirichlet randvoorwaardes, terwyl die vergelyking wat waarnemingsmolekule gedrag by die koppelvlak beskryf bepaalde voorwaardes nodig het. Bakterieë op die grensvlak produseer ook waarnemings-molekules wat diffundeer en afbreek. Om te verseker dat al hierdie eienskappe omvat is in ’n vergelyking is die aanname gemaak dat massa behoud bly. Ter afsluiting is numeriese simulasie van die model gedoen

Transmission of West Nile and Five Other Temperate Mosquito-borne Viruses Peaks at Temperatures Between 23°C and 26°C

The temperature-dependence of many important mosquito-borne diseases has never been quantified. These relationships are critical for understanding current distributions and predicting future shifts from climate change. We used trait-based models to characterize temperature-dependent transmission of 10 vector–pathogen pairs of mosquitoes (Culex pipiens, Cx. quinquefascsiatus, Cx. tarsalis, and others) and viruses (West Nile, Eastern and Western Equine Encephalitis, St. Louis Encephalitis, Sindbis, and Rift Valley Fever viruses), most with substantial transmission in temperate regions. Transmission is optimized at intermediate temperatures (23–26°C) and often has wider thermal breadths (due to cooler lower thermal limits) compared to pathogens with predominately tropical distributions (in previous studies). The incidence of human West Nile virus cases across US counties responded unimodally to average summer temperature and peaked at 24°C, matching model-predicted optima (24–25°C). Climate warming will likely shift transmission of these diseases, increasing it in cooler locations while decreasing it in warmer locations

Transmission of West Nile and Five Other Temperate Mosquito-borne Viruses Peaks at Temperatures Between 23°C and 26°C

The temperature-dependence of many important mosquito-borne diseases has never been quantified. These relationships are critical for understanding current distributions and predicting future shifts from climate change. We used trait-based models to characterize temperature-dependent transmission of 10 vector–pathogen pairs of mosquitoes (Culex pipiens, Cx. quinquefascsiatus, Cx. tarsalis, and others) and viruses (West Nile, Eastern and Western Equine Encephalitis, St. Louis Encephalitis, Sindbis, and Rift Valley Fever viruses), most with substantial transmission in temperate regions. Transmission is optimized at intermediate temperatures (23–26°C) and often has wider thermal breadths (due to cooler lower thermal limits) compared to pathogens with predominately tropical distributions (in previous studies). The incidence of human West Nile virus cases across US counties responded unimodally to average summer temperature and peaked at 24°C, matching model-predicted optima (24–25°C). Climate warming will likely shift transmission of these diseases, increasing it in cooler locations while decreasing it in warmer locations

Long-term health and economic benefits of switching to tenofovir alafenamide versus continuing on entecavir in chronic hepatitis B patients with low-level viremia in Saudi Arabia

Background: Despite the success of current treatments, many chronic hepatitis B (CHB) patients still live with low-level viremia [LLV] resulting in liver disease progression. This study evaluated the long-term health and economic impact of switching to tenofovir alafenamide (TAF) from entecavir (ETV) in Saudi Arabia (SA) in chronic hepatitis B (CHB) LLV patients. Methods: A hybrid decision tree Markov state-transition model was developed to simulate a cohort of patients with CHB LLV treated with ETV and switched to TAF over a lifetime horizon in SA. While on treatment, patients either achieved complete virologic response (CVR) or maintained LLV. CVR patients experienced slower progression to advanced liver disease stages as compared to LLV patients. Demographic data, transition probabilities, treatment efficacy, health state costs, and utilities were sourced from published literature. Treatment costs were sourced from publicly available databases. Results: Base case analysis found that over a lifetime horizon, switching to TAF versus remaining on ETV increased the proportion of patients achieving CVR (76% versus 14%, respectively). Switching to TAF versus remaining on ETV resulted in a reduction in cases of compensated cirrhosis (-52%), decompensated cirrhosis (-5%), hepatocellular carcinoma (-22%), liver transplants (-12%), and a 37% reduction in liver-related deaths. Switching to TAF was cost-effective with an incremental cost-effectiveness ratio of $57,222, assuming a willingness-to-pay threshold of three times gross national income per capita [$65,790/QALY]. Conclusions: This model found that switching to TAF versus remaining on ETV in SA CHB LLV patients substantially reduced long-term CHB-related morbidity and mortality and was a cost-effective treatment strategy