Module 6.5: Malaria

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The malaria model shows the transmission of malaria from vectors for malaria (mosquitoes) to humans. This model contains two parts: stocks and flows for mosquito malaria infection and stocks and flows for human malaria infection.

Let's start with mosquitoes.

Mosquitoes are in two stocks: uninfected mosquitoes and vectors for malaria, who can give the disease to humans. The number of initial uninfected mosquitoes is controlled by a slider. Mosquitoes are born based on a birth rate slider.

After birth, some mosquitoes remain uninfected, bite people, and eventually die, as indicated in the uninfected death rate flow: - (mosquito death rate * uninfected mosquitoes).

Other mosquitoes become infected, as indicated by the infected slider, whihc states that the number of infected mosquitoes equals the probability a mosquito will bite a human (.3) times the probability a mosquito will be a host (initial vectors slider), times the number of uninfected mosquitoes. Once a mosquito is infected and considered a vector for the disease, they can die in the vector deaths slider, whose value is the mosquito death rate times the number of vectors. The total number of mosquitoes is the uninfected mosquitoes plus the vectors.

The model for human infection closely resembles the SIR model, with humans in three different stocks: uninfected, human hosts, and immune. The initial quantities in each stock are controlled by sliders. Humans move from the uninfected stock to the host stock via the flow to host flow. The flow to host occurs based on the probability of being bitten, times the probability of the mosquito that bites them being vectors, times the number of uninfected humans.

Once humans are hosts, three things can happen. They can recover via the recovered flow: - (human hosts * recovery rate). Human hosts can become immune to malaria, via the flow to immune flow: human hosts * immunity rate. Or, human hosts can die, as shown by the human host deaths flow: malaria induced death rate * human hosts.

The graphs show the number of mosquitoes in each state, and the number of humans in each state over time.