A metropolitan city MajCity the capitol of a small country w

A metropolitan city, Maj-City, the capitol of a small country, with a population of 4 million has been designated as a quarantined area by the World Health Organization (WHO) because of an outbreak of pertussis (whooping cough) among its residents. The city agreed to this status because WHO agreed to collect vaccine from stores in other countries, fly it into Maj-City, and administer it to residents who were never vaccinated. Only recently were all children participating in vaccination programs from birth onward. The outbreak of pertussis began after approximately 1000 cases observed among adults of all ages. Very few adults were ever vaccinated because the cost seemed prohibitive and because they were assumed to be already immune.

Please use a SIR-style model to model situations for the officers responsible for the public health of the country, i.e., for the people who perform the work of the CDC in the US. Use a few assumptions

a) Use reasonable parameters from those available online, e.g., see Table 1 at:

b) Consider implementing modern injection methods, e.g., equipment like the US military uses to inoculate military forces going into overseas areas, where 500 individuals can be inoculated per hour per site.
And set up curves to estimate the effects of five, ten, or twenty sites operating in a means to dampen susceptibility and change the dynamics of the outbreak.

c) Assume that the quarantine with the remainder of the country and the outside nations will be effective – food and other necessary supplies will enter, people will not, and only visibly healthy individuals will work at the interface of the two populaces, named city and country.

d) The goal of vaccination is to decrease the number of susceptible individuals. Assume that immunization makes the individual non-susceptible after a set time and allow this portion of the populace to flow to R category with a time constant of n = 3 days after immunization. Design your model to show its data for every day.

e) Assume the vaccinated children in the area make up 20% of the total populace.

People in the countryside are not thought to be in danger. They number about the same as the city, but no census has been carried out in the last two decades. The countryside is very hilly and most roadways are paths for small animal-pulled carts and walking people. The model is not expected to describe the countryside.

As the computationally skilled modeler with WHO, you are asked to describe patterns of infection and its control. These questions are of most interest for a simple SIR model. Answer a and b for the quiz. Answer c and d as a project due the Friday after the quiz.

a) If the pertussis epidemic were to “burn itself out,” which means all possible susceptible people catch pertussis and recover, how long would it take?

b) Assume that numbers of immunization stations greater than 5 were to be established and staffed 16 hours per day. How will these stations change the outcome of the epidemic?

Solution

Ans) a. According to the models, another large-scale epidemic won’t start for at least another ten years—a time when a new generation who hasn’t been exposed to the virus will emerge in the population. This is similar to the way other epidemics work, such as chikungunya (another mosquito-borne disease that’s similar to Zika and dengue), in which explosive epidemics are followed by long periods with few new cases.

b. identify the epidemiologically high-risk communities in a metapopulation network? The network centrality measure, which quantifies the relative importance of each location, is commonly utilized for this purpose. As the disease invasion condition is given from the basic reproductive ratio R₀, we have introduced a novel centrality measure based on the sensitivity analysis of this R₀ and shown its capability of revealing the characteristics that has been overlooked by the conventional centrality measures