Tuberculosis Epidemiology at the Country Scale: Self-Limiting Process and the HIV Effects

<div><p>Background</p><p>The global spread of the human immunodeficiency virus (HIV) is the main hypothesis behind tuberculosis (TB) positive trends in the last decades, according to modeling studies and World Health Organization Reports (WHO). On one hand, TB (WHO) reports do not explicitly consider a modeling approach, but cover country and global TB trends. On the other hand, modeling studies usually do not cover the scale of WHO reports, because of the amount of parameters estimated to describe TB natural history. Here we combined these two principal sources of TB studies covering TB High Burden Countries (HBCs) dynamics. Our main goals were: (i) to detect the endogenous component of TB dynamics since 1974 for TB HBCs; and (ii) to explore the HIV exogenous effects on TB models`parameters.</p><p>Methods and Findings</p><p>We explored the relationship between the TB per capita population rate of change (<i>R</i><sub><i>I</i></sub>) and the infectious class size following an endogenous/exogenous framework. <i>R</i><sub><i>I</i></sub> can be affected by intra-population processes (i.e. competition, predation) and exogenous variables like HIV. We found that TB dynamics had always a strong endogenous component, represented by a negative correlation between TB population size and <i>R</i><sub><i>I</i></sub>, which was captured by the discrete logistic model. Moreover, we explored the HIV exogenous effects on TB models`parameters. We found that overall the TB+HIV logistic model was more parsimonious than TB model alone, principally in the African region. Our results showed that HIV affected principally TB carrying capacity, as expected by the known HIV effects on TB natural-history. We also tested if DOTS (Directly Observed Treatment Short-Course Strategy), poverty levels and BCG (Bacillus Calmette-Guérin) coverage explained the models´ residuals variances, but they did not.</p><p>Conclusions</p><p>Since 1974, TB dynamics were categorized in distinct chronological domains, with different dynamics but nearly the same underlying mechanism: a negative relationship between <i>R</i>_<i>I</i> and infected class size (i.e. self-limiting). In the last decades, not only HIV spread represented a new TB chronological domain, but it also has been pushing TB carrying capacity (<i>K</i>) to higher levels. TB has a complex natural-history and imposes real challenges to model its dynamics. Yet, we were able to explore and reveal the main drivers of TB dynamics for HBCs since 1974, through a simple approach. Based on our results, we suggest that the endogenous view should be considered as a plausible hypothesis to model and explain TB dynamics and that future World Health Organization reports could include the endogenous/exogenous framework as a supplement to help to decipher the main drivers of TB dynamics and other diseases.</p></div

<i>R</i>_<i>I</i>-functions for each country and TB periods of growth for South Africa, Kenya, Mozambique, UR Tanzania, Zimbabwe, Brazil, Bangladesh, Cambodia and China.

<p>The symbols refer to the chronological <i>R</i>_<i>I</i> periods: -○- the first, -Δ- the second, -+- the third and -●- the fourth. Only significant fits for the discrete models are shown with regression lines. <i>R</i>_<i>I</i> negative trends for South Africa and Mozambique over the last years were excluded from <i>R</i>_<i>I</i>-functions and analyses. The first period of TB growth for Tanzania was excluded to properly show the trends of acceleration and decline in <i>R</i>_<i>I</i>. In Brazil, there is a clear cloud of data around zero, suggesting an underlying diminishing returns process between <i>R</i>_<i>I</i> and TB cases.</p

TB time series of South Africa, Kenya, Mozambique, UR Tanzania, Zimbabwe, Brazil, Bangladesh, Cambodia and China since 1974.

<p>Dashed vertical lines refer to the years where time series suffered dynamic changes.</p

TB model parameters for South Africa, Nigeria, Kenya, Mozambique, UR Tanzania, Zimbabwe, Brazil, Bangladesh, Cambodia and China.

<p>TB model parameters for South Africa, Nigeria, Kenya, Mozambique, UR Tanzania, Zimbabwe, Brazil, Bangladesh, Cambodia and China.</p

Spatial autocorrelation analysis of the relative yield losses due to suboptimal water availability (<i>YGRw</i>).

<p>Top: Moran scatterplot; bottom: high-influence areas neighbours: no influence (<i>None</i>), high proportion with low proportion neighbours (<i>HL</i>), the reverse (<i>LH</i>), and both high (<i>HH</i>). We define the break between “low” and “high” as the third quartile.</p

Spatio-Temporal Dynamics of Maize Yield Water Constraints under Climate Change in Spain

<div><p>Many studies have analyzed the impact of climate change on crop productivity, but comparing the performance of water management systems has rarely been explored. Because water supply and crop demand in agro-systems may be affected by global climate change in shaping the spatial patterns of agricultural production, we should evaluate how and where irrigation practices are effective in mitigating climate change effects. Here we have constructed simple, general models, based on biological mechanisms and a theoretical framework, which could be useful in explaining and predicting crop productivity dynamics. We have studied maize in irrigated and rain-fed systems at a provincial scale, from 1996 to 2009 in Spain, one of the most prominent “hot-spots” in future climate change projections. Our new approach allowed us to: (1) evaluate new structural properties such as the stability of crop yield dynamics, (2) detect nonlinear responses to climate change (thresholds and discontinuities), challenging the usual linear way of thinking, and (3) examine spatial patterns of yield losses due to water constraints and identify clusters of provinces that have been negatively affected by warming. We have reduced the uncertainty associated with climate change impacts on maize productivity by improving the understanding of the relative contributions of individual factors and providing a better spatial comprehension of the key processes. We have identified water stress and water management systems as being key causes of the yield gap, and detected vulnerable regions where efforts in research and policy should be prioritized in order to increase maize productivity.</p></div

Definition of study regions (provinces) with percentage of total maize production for 1996–2009.

<p>Only provinces with both irrigated and rain-fed systems were analyzed.</p

Observed numerical fluctuations (ln of number of individuals/m²) of the two weed species; a) <i>Descurainia Sophia</i>; and b) <i>Veronica hederifolia</i> for the no-tillage (blue dots and line) and minimum tillage (red dots and line) systems.

<p>Observed numerical fluctuations (ln of number of individuals/m²) of the two weed species; a) <i>Descurainia Sophia</i>; and b) <i>Veronica hederifolia</i> for the no-tillage (blue dots and line) and minimum tillage (red dots and line) systems.</p

Relative yield losses due to suboptimal water availability (<i>YGRw</i>; <i>%</i>).

<p>The percentage of yield losses due to suboptimal water availability indicates how close rain-fed yield potential are to the irrigated value for a given site.</p

Yield rate of change against the log observed yield level (with one year of delay) and the exogenous factor that perturbs the productivity function (<i>R</i>-function).

<p>Exogenous factors include carbon emissions (<i>CO2_t</i>), precipitation (<i>TPCP_{t_1}</i>), and maximum and minimum temperature (<i>EMXT_{t_1}</i> and <i>EMNT_{t_1}</i>). Additive (vertical) and non-additive (lateral) perturbation effects were detected. Colours indicate the <i>R</i>-function value. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0098220#pone.0098220.s006" target="_blank">Table S1</a> for description of models and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0098220#pone.0098220.s004" target="_blank">Figure S4</a> for their graphs.</p