Fig 1.
Flow diagram representing the transmission dynamics between human and vector populations.
Table 1.
State variables and their descriptions.
Table 2.
Parameters and their biological interpretations of model (1).
Fig 2.
The predicted number of days spent in an egg stage as a function of temperature with a polynomial Regression function of degree two.
Table 3.
Polynomial regression summary for number of days spent in an egg position as a function of temperature.
Fig 3.
The predicted number of days spent in an L1 stage as a function of temperature with a polynomial regression function of degree two.
Fig 4.
The predicted number of days spent in an L2 stage as a function of temperature with a polynomial regression function of degree two.
Fig 5.
The predicted number of days spent in an L3 stage as a function of temperature with a polynomial regression function of degree two.
Fig 6.
The predicted number of days spent in an L4 stage as a function of temperature with a polynomial regression function of degree two.
Fig 7.
The predicted number of days spent in Pupal stage as a function of temperature with a polynomial regression function of degree two.
Fig 8.
Egg mortality rate as a function of temperature with a polynomial regression function of degree two.
Fig 9.
Larvae mortality rate as a function of temperature with a polynomial regression function of degree two.
Fig 10.
Pupae mortality rate as a function of temperature with a polynomial regression function of degree two.
Fig 11.
Adult mortality rate as a function of temperature with a polynomial regression function of degree two.
Table 4.
Summary of temperature-based fitted equations for model parameters with associated goodness-of-fit metrics.
Fig 12.
Time evolution of the human and mosquito compartments in the absence of control interventions.
The susceptible and infected human populations decline rapidly as individuals transition into vaccinated and recovered states.
Fig 13.
Temperature-dependent variation of the basic reproduction number, which peaks at 10.51 when T = 26.1616oC.
The figure highlights the existence of an optimal temperature for malaria transmission, beyond which R0 declines, indicating reduced transmission potential at both lower and higher temperatures.
Fig 14.
Time evolution of model compartments under varying temperature conditions.
The figure shows that temperature value, T = 26.1616oC accelerate transmission dynamics, leading to higher peaks in infection prevalence, indicating the strong temperature sensitivity of malaria spread.
Fig 15.
Sensitivity of mortality rate of mosquitoes and vaccination rate on R0.
Fig 16.
The infected population declines to zero over time for model (1) with the reproduction number indicating that the disease cannot persist and the DFE is globally stable under this threshold.
Fig 17.
The infected population declines to zero over time for model (1) with the reproduction number indicating that the disease cannot persist and the DFE is globally stable under this threshold.
Fig 18.
All trajectories, regardless of initial conditions, converge to the same endemic steady state, confirming the global asymptotic stability of EE for model (1) with the reproduction number .
Fig 19.
All trajectories, regardless of initial conditions, converge to the same endemic steady state, confirming the global asymptotic stability of EE for model (1) with the reproduction number .
Fig 20.
Comparison between model-predicted number of malaria infections and observed infection prevalence data from the Jimma zone as a function of temperature.
Fig 21.
Direct comparison of model predictions from the present model and an existing literature model against observed malaria infection prevalence data from the Jimma zone.
Fig 22.
Side-by-side comparison of monthly infection prevalence predictions from our proposed model and the existing model in [23] against empirical data from the Jimma zone.
Fig 23.
The figure shows that R0 decreases significantly under control strategies, particularly at temperatures near the peak transmission range, indicating the effectiveness of control mechanisms applied.
Fig 24.
Time evolution of infected human and mosquito populations under optimal control compared to the uncontrolled case.
The results demonstrate that applying control strategies significantly reduces infection levels in both populations over time, highlighting the effectiveness of the interventions in mitigating malaria transmission.
Fig 25.
Time evolution of infected human and mosquito populations under optimal control compared to the uncontrolled case.
The results demonstrate that applying control strategies significantly reduces infection levels in both populations over time, highlighting the effectiveness of the interventions in mitigating malaria transmission.
Fig 26.
The solution (infected humans and mosquitoes) of optimal control problem, with and without controls with and c3 = 0 for the first graph and
and c2 = 0 for the second graph.
Fig 27.
The solution (infected humans and mosquitoes) of optimal control problem, with and without controls with and c3 = 0 for the first graph and
and c2 = 0 for the second graph.
Table 5.
Polynomial regression summary for number of days spent in L1 stage as a function of temperature.
Table 6.
Polynomial regression summary for number of days spent in L2 stage as a function of temperature.
Table 7.
Polynomial regression summary for number of days spent in L3 stage as a function of temperature.
Table 8.
Polynomial regression summary for number of days spent in L4 stage as a function of temperature.
Table 9.
Polynomial regression summary for number of days spent in pupal stage as a function of temperature.
Table 10.
Polynomial regression summary for egg mortality rate as a function of temperature.
Table 11.
Polynomial regression summary for larvae mortality rate as a function of temperature.
Table 12.
Polynomial regression summary for pupae mortality rate as a function of temperature.
Table 13.
Polynomial regression summary for adult mortality rate as a function of temperature.