BackgroundIn the weeks following the first imported case of Ebola in the U. S. on September 29, 2014, coverage of the very limited outbreak dominated the news media, in a manner quite disproportionate to the actual threat to national public health; by the end of October, 2014, there were only four laboratory confirmed cases of Ebola in the entire nation. Public interest in these events was high, as reflected in the millions of Ebola-related Internet searches and tweets performed in the month following the first confirmed case. Use of trending Internet searches and tweets has been proposed in the past for real-time prediction of outbreaks (a field referred to as “digital epidemiology”), but accounting for the biases of public panic has been problematic. In the case of the limited U. S. Ebola outbreak, we know that the Ebola-related searches and tweets originating the U. S. during the outbreak were due only to public interest or panic, providing an unprecedented means to determine how these dynamics affect such data, and how news media may be driving these trends.MethodologyWe examine daily Ebola-related Internet search and Twitter data in the U. S. during the six week period ending Oct 31, 2014. TV news coverage data were obtained from the daily number of Ebola-related news videos appearing on two major news networks. We fit the parameters of a mathematical contagion model to the data to determine if the news coverage was a significant factor in the temporal patterns in Ebola-related Internet and Twitter data.ConclusionsWe find significant evidence of contagion, with each Ebola-related news video inspiring tens of thousands of Ebola-related tweets and Internet searches. Between 65% to 76% of the variance in all samples is described by the news media contagion model.
A new non-autonomous model is designed and used to assess the impact of variability in temperature and rainfall on the transmission dynamics of malaria in a population. In addition to adding age-structure in the host population and the dynamics of immature malaria mosquitoes, a notable feature of the new model is that recovered individuals do not revert to wholly-susceptible class (that is, recovered individuals enjoy reduced susceptibility to new malaria infection). In the absence of disease-induced mortality, the disease-free solution of the model is shown to be globally-asymptotically stable when the associated reproduction ratio is less than unity. The model has at least one positive periodic solution when the reproduction ratio exceeds unity (and the disease persists in the community in this case). Detailed uncertainty and sensitivity analysis, using mean monthly temperature and rainfall data from KwaZulu-Natal province of South Africa, shows that the top three parameters of the model that have the most influence on the disease transmission dynamics are the mosquito carrying capacity, transmission probability per contact for susceptible mosquitoes and human recovery rate. Numerical simulations of the model show that, for the KwaZulu-Natal province, malaria burden increases with increasing mean monthly temperature and rainfall in the ranges ([17-25]°C and [32-110] mm), respectively (and decreases with decreasing mean monthly temperature and rainfall values). In particular, transmission is maximized for mean monthly temperature and rainfall in the ranges [21-25]°C and [95-125] mm. This occurs for a six-month period in KwaZulu-Natal (hence, this study suggests that anti-malaria control efforts should be intensified during this period). It is shown, for the fixed mean monthly temperature of KwaZulu-Natal, that malaria burden decreases whenever the amount of rainfall exceeds a certain threshold value. It is further shown (through sensitivity analysis and numerical simulations) that incorporating host age-structure and reduced susceptibility due to prior malaria infection has marginal effect on the transmission dynamics of the disease.
Malaria is mainly a tropical disease and its transmission cycle is heavily influenced by environment: The life-cycles of the Anopheles mosquito vector and Plasmodium parasite are both strongly affected by ambient temperature, while suitable aquatic habitat is necessary for immature mosquito development. Therefore, how global warming may affect malaria burden is an active question, and we develop a new ordinary differential equations-based malaria transmission model that explicitly considers the temperature-dependent Anopheles gonotrophic and Plasmodium sporogonic cycles. Mosquito dynamics are coupled to infection among a human population with symptomatic and asymptomatic disease carriers, as well as temporary immunity. We also explore the effect of incorporating diurnal temperature variations upon transmission. Rigorous analysis of the model show that the non-trivial disease-free equilibrium is locallyasymptotically stable when the associated reproduction number is less than unity (this equilibrium is globally-asymptotically for a special case with no density-dependent larval and disease-induced host mortality). Numerical simulations of the model, for the case where the ambient temperature is held constant, suggest a nonlinear, hyperbolic relationship between the reproduction number and clinical malaria burden. Moreover, malaria burden peaks at 29.5 o C when daily ambient temperature is held constant, but this peak decreases with increasing daily temperature variation, to about 23-25 o C. Malaria burden also varies nonlinearly with temperature, such that small temperature changes influent disease mainly at marginal temperatures, suggesting that in areas where malaria is highly endemic, any response to global warming may be highly nonlinear and most typically minimal, while in areas of more marginal malaria potential (such as the East African highlands), increasing temperatures may translate nearly linearly into increased disease potential. Finally, we observe that while explicitly modelling the stages of the Plasmodium sporogonic cycle is essential, explicitly including the stages of the Anopheles gonotrophic cycle is of minimal importance. ARTICLE HISTORY
Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many parts of the world (notably in Africa, Asia and the Mediterranean). This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations. The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models. In the absence of such phenomenon (which is shown to arise due to the disease-induced mortality in the host populations), the nontrivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality of Brazil, it is shown, for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts, that the associated reproduction number of the model (normalℛ0) ranges from 0.3 to 1.4, with a mean of normalℛ0=0.85. Furthermore, when the effect of such drug treatment is explicitly incorporated in the model (i.e., accounting for the additional larval and sandfly mortality, following feeding on the treated reservoirs), the range of normalℛ0 decreases to normalℛ0∈[0.1,0.25em0.6], with a mean of normalℛ0=0.35 (this significantly increases the prospect of the effective control or elimination of the disease). Thus, ZVL transmission models (in communities where such treatment strategy is implemented) that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of normalℛ0) in the community. It is shown that normalℛ0 is more sensitive to increases in sandfly lifespan than that of the animal reservoir (so, a strategy that focuses on reducing sandflies, rather than the animal reservoir (e.g., via culling), may be more effective in reducing ZVL burden in the community). Further sensitivity analysis of the model ranks the sandfly removal rate (by natural death or by feeding from insecticide-treated reservoir hosts), the biting rate of sandflies on the reservoir hosts and the progression rate of exposed reservoirs to active ZVL as the three parameters with the most effect on the disease dynamics or burden (as measured in terms of the reproduction number normalℛ0). Hence, this study identifies the key parameters that play a key role on the disease dynamics, and thereby contributing in the design of effective control strategies (that target the identified parameters).
Aedes aegypti is the vector for numerous diseases in humans and other (reservoir) hosts, such as chikungunya, dengue fever and Zika virus. A new deterministic model is designed and used to assess the dynamics of the three diseases in a population where Aedes mosquitoes are abundant. The model to be designed incorporates the recently-released imperfect vaccine against dengue virus (Dengvaxia[Formula: see text] vaccine by Sanofi Pasteur) as well as allow for sexual transmission of Zika. Further, the model allows for the assessment of the population-level impact of three biological hypotheses, namely a competitive dengue–chikungunya–Zika superinfection hierarchy, an antibody-dependent enhancement of dengue over Zika and that the Dengvaxia vaccine can induce reduced susceptibility to Zika infection in vaccinated individuals. After carrying out detailed theoretical analyses to gain insight into its qualitative features, the model is then fitted to the data recorded during the 2015–2016 outbreaks of the three diseases in Mexico. Simulations of the model show a reasonable fit to observed dynamics consistent with the competitive hierarchy assumed for the interactions of the viruses. Furthermore, Zika transmission dynamics is only mildly affected by changes in the parameter related to the infectiousness of Zika in relation to dengue, even in the region where antibody-dependent enhancement is assumed. The dengue vaccine has a very marginal impact on Zika transmission dynamics (and that the vaccine, no matter the coverage and efficacy levels, is unable to reduce the reproduction number for Zika transmission to a value less than unity). The model is extended to include the effect of seasonality and local weather variability (temperature and rainfall) on the dynamics of the three diseases. Simulations of the resulting non-autonomous model, using weather and demographic data for Mexico, show that for the current mean monthly rainfall value for Mexico, the burden of the three diseases increases with increasing mean monthly temperature in the range 16–29[Formula: see text]C, and decreases with increasing mean monthly temperature thereafter. Additionally, for the current fixed mean monthly temperature and rainfall data for Mexico, simulations show maximum transmission activity of all three diseases if the temperature and rainfall values lie in the range 25–26.4[Formula: see text]C and 90–128[Formula: see text]mm, respectively (these values are typically recorded in Mexico during the months of June, July and September). Simulations for two Mexican states (Oaxaca and Chiapas) where the three diseases are endemic show maximum transmission activity for all three diseases when temperature and rainfall lie in the ranges 20–25[Formula: see text]C and 51–102[Formula: see text]mm for Oaxaca (these ranges are recorded during the months of May through September) and 19–21[Formula: see text]C and 85–107[Formula: see text]mm for Chiapas (there ranges are recorded during the months of May, July, August and October), respectively. These simulations suggest suitable time when anti-mosquito control efforts should be intensified in Mexico (and the two selected states).
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