|
|
 |
| |
|
|
|
Co-Dynamics of Trypanosomiasis and Cryptosporidiosis |
|
|
|
PP: 2137-2161 |
|
|
|
doi:10.18576/amis/100617
|
|
|
|
Author(s) |
|
|
|
Kazeem Oare Okosun,
Mirirai Mukamuri,
Oluwole Daniel Makinde,
|
|
|
|
Abstract |
|
|
| In this paper a mathematical model for trypanosomiasis-cryptosporidium co-infection dynamics is investigated to give
a theoretical mathematical account of the impact of cryptosporidiosis on trypanosomiasis dynamics. The model steady states are
analyzed. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic basic reproduction
number for the model is less than unity. The trypanosomiasis only and the cryptosporidiosis only model are each found to exhibit
transcritical and backward bifurcation phenomena respectively. While the co-infection model exhibits the possibility of multiple
endemic equilibria. From the sensitivity analysis, the trypanosomiasis reproductive number Rlt
0 is more sensitive to d (death due to
insecticides) and crypto parameters whenever Rcr
0 > 1 (crypto reproductive number). While the cryptosporidiosis reproductive number
Rcr
0 is less sensitive to trypanosomiasis parameters whenever Rlt
0 > 1 (trypanosomiasis reproductive number). This is an indication
that cryptosporidiosis infection may be associated with an increased risk of trypanosomiasis, while trypanosomiasis infection is not
associated with an increased risk for cryptosporidiosis.We incorporate time dependent controls, using Pontryagin’sMaximum Principle
to derive necessary conditions for the optimal control of the disease. Furthermore, the effect of the presence of each infection on the
endemicity of the other is investigated and presented numerically. |
|
|
|
|
|
|
|
