Modeling the Effectiveness of TV and Social Media Advertisements on the Dynamics of Water-Borne Diseases

Cholera is a serious threat to the health of human-kind all over the world and its control is a problem of great concern. In this context, a nonlinear mathematical model to control the prevalence of cholera disease is proposed and analyzed by incorporating TV and social media advertisements as a dynamic variable. It is considered that TV and social media ads propagate the knowledge among the people regarding the severe effects of cholera disease on human health along with its precautionary measures. It is also assumed that the mode of transmission of cholera disease among susceptible individuals is due to consumption of contaminated drinking water containing Vibrio cholerae. Moreover, the propagation of knowledge through TV and social media ads makes the people aware to adopt precautionary measures and also the aware people make some effectual efforts to washout the bacteria from the aquatic environment. Model analysis reveals that increase in the washout rate of bacteria due to aware individuals causes the stability switch. It is found that TV and social media ads have the potential to reduce the number of infectives in the region and thus control the cholera epidemic. Numerical simulation is performed for a particular set of parameter values to support the analytical findings.

Optimal control of vaccination rate in an epidemiological model of Clostridium difficile transmission

The spore-forming, gram-negative bacteria Clostridium difficile can cause severe intestinal illness. A striking increase in the number of cases of C. difficile infection (CDI) among hospitals has highlighted the need to better understand how to prevent the spread of CDI. In our paper, we modify and update a compartmental model of nosocomial C. difficile transmission to include vaccination. We then apply optimal control theory to determine the time-varying optimal vaccination rate that minimizes a combination of disease prevalence and spread in the hospital population as well as cost, in terms of time and money, associated with vaccination. Various hospital scenarios are considered, such as times of increased antibiotic prescription rate and times of outbreak, to see how such scenarios modify the optimal vaccination rate. By comparing the values of the objective functional with constant vaccination rates to those with time-varying optimal vaccination rates, we illustrate the benefits of time-varying controls.

A REACTION–DIFFUSION MODEL FOR THE CONTROL OF CHOLERA EPIDEMIC

Understanding the spatio-temporal dynamics of cholera outbreaks may help in devising more effective control procedures. In this paper, we have considered a reaction–diffusion system for biological control of cholera epidemic. Firstly, we have focused on temporal evolution of cholera in a region and its control using lytic bacteriophage in the aquatic reservoirs. Then, we have explored the effect of spatial dispersion of populations on the disease dynamics. We have observed the onset of sustained oscillations via Hopf-bifurcation for the endemic state of temporal system. This onset of fluctuations in populations depends upon the phage adsorption rate. But in the spatially extended setting, all the populations stabilize i.e., the spatio-temporal distribution of all the populations becomes uniform. Some numerical computations have been done to verify analytical results.