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All Journal Jambura Journal of Biomathematics (JJBM) ARRUS Journal of Mathematics and Applied Science
Ochwach, Jimrise
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Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Physics

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Mathematical Model of the Impact of Home-Based Care on Contagious Respiratory Illness Under Optimal Conditions Wanjala, Henry Milimo; Okongo, Mark; Ochwach, Jimrise
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 2: December 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i2.27611

Abstract

Mathematical models are vital for understanding real-world phenomena without direct experimentation, particularly in epidemics, as they predict and analyze the effectiveness of various mitigation strategies. Given the rapid transmission of infectious respiratory diseases, public health measures aim to curb spread while managing impacts. This study assesses rapid contact tracing and testing, focusing on isolating confirmed cases through home-based care or traditional methods, on coronavirus transmission within a community.A deterministic mathematical model using ordinary differential equations segments the population into seven compartments: susceptible, exposed, asymptomatic, symptomatic, home-based care, hospitalized, and recovered. The basic reproduction number is determined via the next generation matrix. Local stability of the disease-free equilibrium is analyzed using the trace-determinant method, while global stability is confirmed with the Lyapunov-Krasovskii approach. A Python-based numerical simulation on NumPy and PyPlot uses parameters calibrated to previous studies and estimated for this research. Simulations indicate home-based care delays peak infection days and reduces peak population, providing time to bolster healthcare facilities. Optimal control methods, including media awareness, reduce susceptibility and encourage asymptomatic individuals to choose home-based care. Using Pontryagin's Maximum Principle, the study identifies optimal strategies, highlighting that media awareness effectively lowers susceptibility and optimal control directs asymptomatics to home-based care, reducing strain on healthcare facilities. In conclusion, home-based care is effective for managing mild symptomatic and asymptomatic cases, alleviating pressure on healthcare resources and prioritizing severe cases. Combining home-based care with other non-pharmaceutical strategies is recommended for maximum effectiveness.
Bifurcation Analysis of an Infectious Respiratory Disease with Lockdown and Social Distancing Wanjala, Henry; Okongo, Mark; Ochwach, Jimrise
ARRUS Journal of Mathematics and Applied Science Vol. 4 No. 2 (2024)
Publisher : PT ARRUS Intelektual Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35877/mathscience3033

Abstract

This paper analyzes the impact of lockdown, social distancing, and isolation of symptomatic patients on the transmission of infectious respiratory diseases. The study uses predictive mathematical models to explore disease progression and evaluate control strategies. The results show that the disease-free equilibrium is locally stable but globally unstable, indicating that while these measures can slow the infection, they alone cannot eradicate the disease. Local stability was assessed using the determinant-trace matrix method, while global stability was analyzed through the Lyapunov-Krasovskii method, revealing instability around the global endemic equilibrium. Bifurcation analysis was conducted to identify critical points where small parameter changes could cause significant shifts in system behavior. Numerical simulations were performed using Python’s NumPy and PyPlot libraries to understand the dynamics of disease spread and evaluate various intervention strategies. The simulations demonstrated how changes in control measures affect the disease’s trajectory. In the absence of effective treatments or vaccines, the findings suggest that social distancing, lockdowns, and isolation are vital for controlling the spread of the pandemic and reducing mortality. These strategies will be essential for mitigating the impact of the disease in the short term.
Co-Authors Okongo, Mark Wanjala, Henry Wanjala, Henry Milimo