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Modelo SEIR-t
Storyboard

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ID:(572, 0)


Specific mortality with malaria
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The specific mortality of a person with malaria shows that it is a disease that primarily attacks children and the elderly. The attached graphic, from the study ['How Many Years of Life Could Be Saved If Malaria Were Eliminated from a Hyperendemic Area of Northern Ghana?'] (Http://www.gphysics.net/downloads/medicine/Bookshelf_NBK1712.pdf) Ayaga A. Bawah and Fred N. Binka shows mortality according to age with and without malaria:

ID:(8215, 0)


Life expectancy with malaria
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The average life expectancy of a person with malaria is reduced on average by approximately 10 years. The attached graphic, from the study ['How Many Years of Life Could Be Saved If Malaria Were Eliminated from a Hyperendemic Area of Northern Ghana?'] (Http://www.gphysics.net/downloads/medicine/Bookshelf_NBK1712.pdf) Ayaga A. Bawah and Fred N. Binka shows life expectancy according to age with and without malaria:

ID:(8214, 0)


Statistics of mosquito and bite populations
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In the article ['Human-to-mosquito transmission effciency increases as malaria is controlled'] (http://www.gphysics.net/downloads/medicine/Churcher_et_al-2015-Nature_Communications.pdf) by Thomas S. Churcher, Jean- Francois Trape and Anna Cohuet in Nature Communications published on January 19, 2015 look at the curves seen in the image below:

We rescue that the fraction of mosquitoes V/N_V is of the order of 3% while that of the human in zones of epidemic I/N_I is of the order of 20 to 30%.

On the other hand about 30 bites per month are observed. Therefore the probability of daily bite p_b is of the order of 1 per day.

If you think about measures you can study the years in which the number of bites receded and determine the cause of this. As an example, if it were detected that in a year of drought the rate falls, it could be concluded that with drainage measures, areas prone to inhabit mosquitoes with malaria can be dried. In this case, the data of said favorable years can be taken to determine a set of data that would be given in the case of taking measures. This is how a reduction of 30 to 15 bites per month would lead to measures that the probability of being bitten p_b falls from 1 / day (30/30) to 0.5 / day (15/30).

Note: It is important to keep in mind that the p_b factor depends on the mosquito population, the human population and the circumstances that allow the mosquito to have access to the human. In other words, the value of a bite per human, mosquito and day depends on the circumstances.

ID:(8199, 0)


Estimation of human contagion probabilities
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If the asymptotic situation of a population of humans with malaria is known, the equations can be used

$i_{\infty}=\displaystyle\frac{\Lambda p_b^2p_Ip_V-\mu\gamma}{p_bp_V(\gamma+\Lambda p_bp_I)}$



and

$v_{\infty}=\displaystyle\frac{\Lambda p_b^2p_Ip_V-\mu\gamma}{\Lambda p_bp_I(\mu+p_bp_V)}$



to determine p_I. When clearing you get like this

$p_i=\displaystyle\frac{\gamma i}{(1-i)p_b v \Lambda}$

ID:(8211, 0)


Estimation of mosquito contagion probabilities
Equation

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If the asymptotic situation of a population of humans with malaria is known, the equations can be used

$i_{\infty}=\displaystyle\frac{\Lambda p_b^2p_Ip_V-\mu\gamma}{p_bp_V(\gamma+\Lambda p_bp_I)}$



and

$v_{\infty}=\displaystyle\frac{\Lambda p_b^2p_Ip_V-\mu\gamma}{\Lambda p_bp_I(\mu+p_bp_V)}$



to determine p_v. When clearing you get like this

$p_v=\displaystyle\frac{\mu v}{p_b i(1-v)}$

ID:(8212, 0)


Country statistics
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Population:

Year | Sick | Deaths

: -----: |: -------: |: ---------:

2000 | 3349528 | 6108 |

2001 | 3044844 | 1717 |

2002 | 3140893 | 2376 |

2003 | 3552896 | 2103 |

2004 | 3416033 | 1575 |

2005 | 3452969 | 2037 |

2006 | 3511452 | 3125 |

2007 | 3123147 | 4622 |

2008 | 3200147 | 3889 |

2009 | 3694671 | 3378 |

2010 | 3849536 | 3859 |

2011 | 4154261 | 3259 |

2012 | 10676731 | 2855 |

2013 | 7200797 | 2506 |

2014 | 8453557 | 2200 |

ID:(9664, 0)


Probability estimate
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If it is assumed that the number of bites is one per day (p_b\sim 1), half of the mosquitoes are female (\Lambda\sim 0.5), the fraction of infected mosquitoes is of the order of 3% (i) and 30% of humans (v), the life expectancy of a person with malaria 49 years (\gamma\sim 1/(365 * 49) = 5.6\times 10<{-5}) and the half-life of a 31-day mosquito (\mu\sim 1/31=0.0322) you have with

$p_i=\displaystyle\frac{\gamma i}{(1-i)p_b v \Lambda}$



that p_I is of the order of 0.001114 and with

$p_v=\displaystyle\frac{\mu v}{p_b i(1-v)}$

that p_V is of the order of 0.003320.

ID:(8213, 0)


Malaria Simulator
Php

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The simulator for the case of malaria allows to experiment with the different parameters and observe how the populations of infected humans and mosquitoes develop:

ID:(9660, 0)