(Lecture by Prof Eduardo Massad, Mathematical Models of Dengue Fever) This lecture touches on the topic of modeling for dengue fever, yellow fever and chikungunya. Geographical applications abound both for areas in Brazil and in Singapore. Vaccination strategies could depend on such models to acquire a more effective result, as this model suggests a parameter Pc, the critical proportion of a population to be vaccinated to prevent an epidemical outbreak of these respective viral diseases. Limitations to the model are discussed, such as the temperature dependence of the parameters of the model are considered, and especially with regard to increasing global temperatures due to global warming. Description of models discussed in lecture
Prof Massad first mentions the parameter Ro, the basic reproduction number, defined as the number of secondary infections produced by a single infective in an entire susceptible population (Macdonald, 1952). Ro= ma2bcexp-μ nr μ
a:average daily biting rate of the vector,
c:the mosquito’s susceptibility,
µ:the vector mortality rate,
n:the parasite extrinsic incubation period, in days,|
r:the parasitemia recovery rate. (Massad et. al., 2001)
However, this equation for Ro is valid for simple cases where there is only one vector or breed of mosquitoes, and one host (i.e. humans). The resulting equation derived for more complex systems is thus Ro= aNmaNHraexp-μ τ b cμ
whereNm :number of female mosquitoes.
a: daily biting rate female mosquitoes inflict on the human population. NH:number of humans.
r:rate of recovery from parasitemia in the human cases
c: probability that a mosquito gets the infection after biting an infective human. b:probability that a human gets the infection after being bitten by an infective mosquito e-µτ:fraction of infected mosquito population that survives through the extrinsic incubation period, τ, of the parasite. Subsequent...