State variables, parameters definitions and values used in the model.

<p>Where two numbers are listed for <i>ψ</i>, they indicate the values used for TF 40% and 20% communities.</p

Estimates from the best performing models of the age-specific PCR and TF prevalence.

<p>Estimates of age-specific TF and PCR prevalence from statistically the best performing models for each structure evaluated. Data is shown in red, Model 1 results are shown in purple, Model 2 results are shown in blue, Model 3 results are shown in green, and Model 4 results are shown in pink. The first row shows PCR and TF fits from the 4 parameter models. The second row shows PCR and TF fits from the 3 parameter model. Lines around each model’s point estimate are the 95% credible intervals.</p

Schematic of the different model structures evaluated.

<p>A) Represents Model 1, here individuals in the <i>D</i> are 100% immune to re-infection. B) Represents Model 2, where individuals in the <i>D</i> state can be re-infected. C) Represents Model 3 [<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0005378#pntd.0005378.ref018" target="_blank">18</a>], where individuals are 100% immune to re-infection in the <i>D</i> state but can be re-infected once they progress to the <i>PD</i> state. D) Represents Model 4 where individuals in the <i>IO</i> state spend a period of time only PCR positive, then progress to <i>ID</i> where they are PCR and TF positive. Coloured arrows illustrate how treatment within each model structure is implemented. Individuals who are infected but not infectious when treated return to the <i>S</i>_<i>i</i> class they were in before they were infected (indicated by the red arrow), hence no immunity is acquired as a result of infection. For those in the <i>ID</i>_<i>i</i> or <i>IO</i>_<i>i</i> class who are successfully treated they progress to the <i>D</i> (indicated by the green arrow) and were assumed to acquire immunity as a consequence of the infection they experienced. Treatment was assumed to not impact those in the disease only states. The (*) around parameters indicate that the minimum rate of recovery of these parameters was estimated.</p

Prevalence of TF in 0–9 year olds when MDA has been applied for 3 annual rounds for 3 years within a community with 20% TF prevalence.

<p>A) Model 2 assuming 20% susceptibility to re-infection in the <i>D</i> and assuming an individual’s infectivity decayed exponentially with each successive infection. B) Model 3 assuming 20% susceptibility to re-infection in the <i>PD</i> and assuming an individual’s infectivity decayed exponentially with each successive infection. C) Model 4 assuming 80% susceptibility to re-infection in the <i>D</i> and assuming an individual’s infectivity decayed exponentially with each successive infection. D) Model 2 assuming 20% susceptibility to re-infection in the <i>D</i> and assuming a linear decline in infectivity with each successive infection. E) Model 3 assuming 20% susceptibility to re-infection in the <i>PD</i> and assuming a linear decline in infectivity with each successive infection. F) Model 4 assuming 80% susceptibility to re-infection in the <i>D</i> and assuming a linear decline in infectivity with each successive infection. For the 4 and 3 parameter versions of Models 2–4 (A–F) we considered variable reductions in the transmission rate <i>β</i> that may be achievable through facial cleanliness and environmental improvements (F&E). We consider instantaneous non-linear declines in <i>β</i> across the 5 year intervention period. We considered maximum reductions in <i>β</i> over the 3 year intervention period to be 0, 10, 30 or 50% from the initial value used.</p

Additional file 1: of Enhanced antibiotic distribution strategies and the potential impact of facial cleanliness and environmental improvements for the sustained control of trachoma: a modelling study

Additional detail on modelling methods and sensitivity analyses. (PDF 3614 kb

Dependence of <i>R₀^M</i> on LF prevalence in hosts for different mosquito biting rates.

<p>Dependence of <i>R₀^M</i> on LF prevalence in hosts for different mosquito biting rates.</p

Modelling Co-Infection with Malaria and Lymphatic Filariasis

<div><p>Malaria and lymphatic filariasis (LF) continue to cause a considerable public health burden globally and are co-endemic in many regions of sub-Saharan Africa. These infections are transmitted by the same mosquito species which raises important questions about optimal vector control strategies in co-endemic regions, as well as the effect of the presence of each infection on endemicity of the other; there is currently little consensus on the latter. The need for comprehensive modelling studies to address such questions is therefore significant, yet very few have been undertaken to date despite the recognised explanatory power of reliable dynamic mathematical models. Here, we develop a malaria-LF co-infection modelling framework that accounts for two key interactions between these infections, namely the increase in vector mortality as LF mosquito prevalence increases and the antagonistic Th1/Th2 immune response that occurs in co-infected hosts. We consider the crucial interplay between these interactions on the resulting endemic prevalence when introducing each infection in regions where the other is already endemic (e.g. due to regional environmental change), and the associated timescale for such changes, as well as effects on the basic reproduction number <i>R₀</i> of each disease. We also highlight potential perverse effects of vector controls on human infection prevalence in co-endemic regions, noting that understanding such effects is critical in designing optimal integrated control programmes. Hence, as well as highlighting where better data are required to more reliably address such questions, we provide an important framework that will form the basis of future scenario analysis tools used to plan and inform policy decisions on intervention measures in different transmission settings.</p></div

Invasion of (a and b) malaria in LF endemic regions, and (c and d) LF in malaria endemic regions.

<p>Prevalence time-series, in hosts and vectors, when introducing malaria or LF into endemic regions of the other.</p

Structure of the full malaria-LF co-infection model.

<p>(NB. Life stage transition arrows from each <i>L</i> compartment to each <i>W</i> compartment should also strictly be present, but these are omitted here for clarity. All birth and deaths rates are also omitted, as well as the labelling of rates in terms of model parameters).</p

Parameters of the full co-infection model.

<p>Parameters of the full co-infection model.</p