# A Mathematical Model for the Effect of Domestic Animals on the Basic Reproduction Number of Human African Trypanosomiasis (Sleeping Sickness)

## Disciplines

Applied Mathematics | Ordinary Differential Equations and Applied Dynamics

## Abstract (300 words maximum)

The Human African Trypanosomiasis (HAT) parasite, which causes African Sleeping Sickness, is transmitted by the tsetse fly as a vector (which passes on the parasite, but does not contract the disease). It has several possible hosts, including humans and domestic animals, which are affected by the disease when bitten by an infected fly. It has long been assumed, because domestic animals can be a host for the parasite, that keeping domestic animals near human populations increases the spread of the disease. However, several parameters found in the literature, including the shorter lifespan of the male vector and the female vector's preference for domestic animals, made us question this assumption.

We have developed a differential equation compartmental model to examine whether increasing the domestic animal population can be used to deflect the infection from humans and reduce its impact. This 9-dimensional system of nonlinear ordinary differential equations includes tsetse flies in their various stages of maturity, which is more than most previous models have done. We have calculated R0, known as the basic reproduction number. This R0 can tell us whether the disease will spread and become an epidemic, or not. We used an advanced technique known as the Next Generation Matrix method to obtain an expression for R0 based on the other parameters in the model.

Our study indicates that strategies that were not previously considered, such as vaccinating domestic animals, may reduce the impact of the disease on humans even better than vaccinating humans.

## Academic department under which the project should be listed

CSM - Mathematics

## Primary Investigator (PI) Name

Meghan Burke, D.Phil.

## Share

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A Mathematical Model for the Effect of Domestic Animals on the Basic Reproduction Number of Human African Trypanosomiasis (Sleeping Sickness)

The Human African Trypanosomiasis (HAT) parasite, which causes African Sleeping Sickness, is transmitted by the tsetse fly as a vector (which passes on the parasite, but does not contract the disease). It has several possible hosts, including humans and domestic animals, which are affected by the disease when bitten by an infected fly. It has long been assumed, because domestic animals can be a host for the parasite, that keeping domestic animals near human populations increases the spread of the disease. However, several parameters found in the literature, including the shorter lifespan of the male vector and the female vector's preference for domestic animals, made us question this assumption.

We have developed a differential equation compartmental model to examine whether increasing the domestic animal population can be used to deflect the infection from humans and reduce its impact. This 9-dimensional system of nonlinear ordinary differential equations includes tsetse flies in their various stages of maturity, which is more than most previous models have done. We have calculated R0, known as the basic reproduction number. This R0 can tell us whether the disease will spread and become an epidemic, or not. We used an advanced technique known as the Next Generation Matrix method to obtain an expression for R0 based on the other parameters in the model.

Our study indicates that strategies that were not previously considered, such as vaccinating domestic animals, may reduce the impact of the disease on humans even better than vaccinating humans.