Browsing by Author "Helikumi , Mlyashimbi"

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Mathematical modeling and optimization of monocyte-driven immune dynamics and treatment strategies in within-host Mycobacterium tuberculosis
(MATHEMATICS IN MEDICAL AND LIFE SCIENCES, 2026-03-23) Helikumi , Mlyashimbi; Mushayabasa, Steady
Tuberculosis (TB) remains a major global health challenge, driven by complex within-host interactions between Mycobacterium tuberculosis (Mtb) and the host immune system. To better understand these dynamics, we develop a mathematical model that incorporates monocytes, macrophages, and T lymphocytes. Analytical results show that the basic repro- duction number, R0, depends on key infection and immune-response parameters and can exceed unity under biologically plausible conditions, leading to persistent infection. Bifur- cation analysis reveals the occurrence of a backward bifurcation at R0 = 1, indicating that reducing R0 below unity may not be sufficient for disease eradication, as stable endemic equilibria can coexist with the disease-free equilibrium when R0 < 1. Numerical simu- lations under baseline parameter values demonstrate that enhancing immune response parameters substantially lowers bacterial burden, reducing bacterial populations by up to 70% within 60 days, whereas increased infection rates accelerate disease progression, doubling bacterial populations in approximately half the time. Furthermore, an optimal control analysis suggests that, under representative treatment scenarios, intensified drug treatment can reduce bacterial loads by more than 90% within 30 days; however, com- plete bacterial clearance may remain unattainable because of the backward bifurcation phenomenon. These findings underscore the importance of integrating immune enhance- ment with optimized treatment strategies and highlight that achieving R0 < 1 alone may not guarantee eradication of TB infection.
Modeling the implications of seasonality and heterogeneous mean worm burden in Guinea-worm disease dynamics in dog population.
(Nonlinear Science, 2025-05-09) Lusekelo ,Eva; Daudi ,Salamida; Helikumi , Mlyashimbi; Mushayabasa, Steady
Prior to 2012, it was believed that only humans could host Guinea-worm disease. Recent findings show that dogs also act as hosts. With the 2030 goal for eradicating Guinea-worm approaching, understanding dogs’ roles is crucial. We develop a mathematical model to study seasonal Guinea-worm disease, focusing on dogs as primary hosts, given the low human cases. Our model includes seasonal variations, as previous studies indicate that disease prevalence is linked to seasonal fisheries. We also categorize infectious dogs based on their average worm burden. Our analysis examines how dog screening and tethering influence disease dynamics. Results indicate that both strategies can lower disease transmission. However, they may not be enough for total eradication on their own. Therefore, we suggest combining these methods with additional actions, like dog culling, to improve disease control.