Modeling the Effect of TV and Social Media Advertisements on the Dynamics of Vector-Borne Disease Malaria

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Abstract

Vector-borne disease malaria is transmitted to humans by arthropod vectors (mosquitoes) and contributes significantly to the global disease burden. TV and social media play a key role to disseminate awareness among people by broadcasting awareness programs. In this paper, a nonlinear model is formulated and analyzed in which cumulative number of advertisements through TV and social media is taken as dynamical variable that propagates awareness among people to control the prevalence of vector-borne disease. The human population is partitioned into susceptible, infected and aware classes, while the vector population is divided into susceptible and infected classes. Humans become infected and new cases arise when bitten by infected vectors (mosquitoes) and susceptible vectors get infected as they bite infected humans. The feasibility of equilibria is justified and their stability conditions are discussed. A crucial parameter, basic reproduction number, which measures the disease transmission potentiality is obtained. Bifurcation analysis is performed by varying the sensitive parameters, and it is found that the proposed system shows different kinds of bifurcations, such as transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation, etc. The analysis of the model shows that reduction in vector population due to intervention of people of aware class would not efficiently reduce the infective cases, rather we have to minimize the transmission rates anyhow, to control the disease outbreak.

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Modelling the influence of human behaviour on the spread of infectious diseases: a review.

Sebastian Funk, Marcel Salathé, Vincent A. A. Jansen (2010)

Human behaviour plays an important role in the spread of infectious diseases, and understanding the influence of behaviour on the spread of diseases can be key to improving control efforts. While behavioural responses to the spread of a disease have often been reported anecdotally, there has been relatively little systematic investigation into how behavioural changes can affect disease dynamics. Mathematical models for the spread of infectious diseases are an important tool for investigating and quantifying such effects, not least because the spread of a disease among humans is not amenable to direct experimental study. Here, we review recent efforts to incorporate human behaviour into disease models, and propose that such models can be broadly classified according to the type and source of information which individuals are assumed to base their behaviour on, and according to the assumed effects of such behaviour. We highlight recent advances as well as gaps in our understanding of the interplay between infectious disease dynamics and human behaviour, and suggest what kind of data taking efforts would be helpful in filling these gaps.

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The spread of awareness and its impact on epidemic outbreaks.

Sebastian Funk, Erez Gilad, Chris Watkins … (2009)

When a disease breaks out in a human population, changes in behavior in response to the outbreak can alter the progression of the infectious agent. In particular, people aware of a disease in their proximity can take measures to reduce their susceptibility. Even if no centralized information is provided about the presence of a disease, such awareness can arise through first-hand observation and word of mouth. To understand the effects this can have on the spread of a disease, we formulate and analyze a mathematical model for the spread of awareness in a host population, and then link this to an epidemiological model by having more informed hosts reduce their susceptibility. We find that, in a well-mixed population, this can result in a lower size of the outbreak, but does not affect the epidemic threshold. If, however, the behavioral response is treated as a local effect arising in the proximity of an outbreak, it can completely stop a disease from spreading, although only if the infection rate is below a threshold. We show that the impact of locally spreading awareness is amplified if the social network of potential infection events and the network over which individuals communicate overlap, especially so if the networks have a high level of clustering. These findings suggest that care needs to be taken both in the interpretation of disease parameters, as well as in the prediction of the fate of future outbreaks.

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The construction of next-generation matrices for compartmental epidemic models.

O. Diekmann, J. A. P. Heesterbeek, M. G. Roberts (2010)

The basic reproduction number (0) is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of (0) where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used so-called compartmental models. We present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be the NGM with large domain and the NGM with small domain. The three matrices together reflect the range of possibilities encountered in the literature for the characterization of (0). We show how they are connected and how their construction follows from the basic model ingredients, and establish that they have the same non-zero eigenvalues, the largest of which is the basic reproduction number (0). Although we present formal recipes based on linear algebra, we encourage the construction of the NGM by way of direct epidemiological reasoning, using the clear interpretation of the elements of the NGM and of the model ingredients. We present a selection of examples as a practical guide to our methods. In the appendix we present an elementary but complete proof that (0) defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties that (0) > 1 if and only if r > 0, and (0) = 1 if and only if r = 0.