Authors :
Lawal Jibril; Samaila Musa
Volume/Issue :
Volume 8 - 2023, Issue 3 - March
Google Scholar :
https://bit.ly/3TmGbDi
Scribd :
https://bit.ly/3Mirgsj
DOI :
https://doi.org/10.5281/zenodo.7797254
Abstract :
This paper provides a rigorous
mathematical and sensitivity analysis on the cholera
epidemic model with vaccination. The model consists of
six system of nonlinearly differential equation. The
basic properties of the model for positivity of solutions
were investigated which the solution
S t
,
E t
,
I t
,
V t
,
R t
and
P t
are found to be nonnegative
for
t 0
. Existence and uniqueness of the model
reveals that there exist a unique solution which is
bounded and continuous in region
D
. The theoretical
analysis of the model reveals that cholera will dies out
whenever the threshold quantity
R0
is less than unity
and it will persists in the community if otherwise The
sensitivity analysis was performed around the baseline
parameter value. The result shows that the contact rate
in human
1
with the value 0.6868, and the shedding
rate
with the value 0.5901 are the most sensitive
parameter that influenced the threshold quantity
R0
.
Furthermore it was observed that any increase in the
following parameter
2
results in the increase of
R0
. Similarly, increase in the following parameter
1 2
1
decrease the threshold quantity
R0
. The
numerical simulation using an arbitrary set of
parameter values were carried out and plotted in which
the results for sensitivity analysis and threshold
criterion were found to be in agreement with analytical
results shown in Table 3 and Theorem 2.
Keywords :
Cholera epidemic Model; differential equation; sensitivity analysis; threshold quantity; Vaccination.
This paper provides a rigorous
mathematical and sensitivity analysis on the cholera
epidemic model with vaccination. The model consists of
six system of nonlinearly differential equation. The
basic properties of the model for positivity of solutions
were investigated which the solution
S t
,
E t
,
I t
,
V t
,
R t
and
P t
are found to be nonnegative
for
t 0
. Existence and uniqueness of the model
reveals that there exist a unique solution which is
bounded and continuous in region
D
. The theoretical
analysis of the model reveals that cholera will dies out
whenever the threshold quantity
R0
is less than unity
and it will persists in the community if otherwise The
sensitivity analysis was performed around the baseline
parameter value. The result shows that the contact rate
in human
1
with the value 0.6868, and the shedding
rate
with the value 0.5901 are the most sensitive
parameter that influenced the threshold quantity
R0
.
Furthermore it was observed that any increase in the
following parameter
2
results in the increase of
R0
. Similarly, increase in the following parameter
1 2
1
decrease the threshold quantity
R0
. The
numerical simulation using an arbitrary set of
parameter values were carried out and plotted in which
the results for sensitivity analysis and threshold
criterion were found to be in agreement with analytical
results shown in Table 3 and Theorem 2.
Keywords :
Cholera epidemic Model; differential equation; sensitivity analysis; threshold quantity; Vaccination.
