Analytical Model for Malaria
The human population is divided into four classes: Susceptible, Exposed, Infectious, and Recovered.
When an infectious mosquito bites a susceptible person, there is a probability that the parasite (sporozoites) will be passed into the human which will move them to the exposed class. The parasite then travels to the liver, where it will develop to the next life stage. Over a period of time the parasite (has now turned into merozoites) enters the blood stream which signals the clinical onset of malaria. The human has now become a part of the infectious class. After a certain period of time, the infectious human recovers and become a part of the recovered class which will eventually lead them back to the susceptible class.
The mosquito population is divided into three classes: Susceptible, Exposed, and Infectious.
The parasite enters the mosquito when it bites an infectious or recovering human; the mosquito is now in the exposed classed. After some period of time, depending on temperature and humidity, the parasite develops into sporozoites and enters the mosquitos salivary glands; the mosquito is now in the infectious class for life.
When an infectious mosquito bites a susceptible person, there is a probability that the parasite (sporozoites) will be passed into the human which will move them to the exposed class. The parasite then travels to the liver, where it will develop to the next life stage. Over a period of time the parasite (has now turned into merozoites) enters the blood stream which signals the clinical onset of malaria. The human has now become a part of the infectious class. After a certain period of time, the infectious human recovers and become a part of the recovered class which will eventually lead them back to the susceptible class.
The mosquito population is divided into three classes: Susceptible, Exposed, and Infectious.
The parasite enters the mosquito when it bites an infectious or recovering human; the mosquito is now in the exposed classed. After some period of time, depending on temperature and humidity, the parasite develops into sporozoites and enters the mosquitos salivary glands; the mosquito is now in the infectious class for life.
Malaria Model (Variables and Parameters)
Infection Rate
Model of Mosquito Bites on Humans
The total number of mosquito-human contacts depends on the populations of both species.
Reproductive number
The reproductive number: The amount of secondary infections that an infectious person would create over a period of time during the infectious period, provided that everyone else is susceptible.
These two variables are defined as the probability of transmission per contact and survival until reach the infectious state, the number of contacts per unit time, and the duration of the infectious period:
Reference
1. Chitnis, Nakul, J. M. Cushing, and J. M. Hyman. "Bifurcation Analysis of a Mathematical Model for Malaria Transmission." Society for Industrial and Applied Mathematics, 2006. Web. 16 Nov. 2012. <http://math.arizona.edu/~cushing/BifurcationAnalysisOfModelForMalaria%20SIAP06.pdf>.