A Mathematical Model for the Transmission of Giardiasis Incorporating Resistance Strain and Second Line of Treatment
DOI:
https://doi.org/10.62054/ijdm/0303.07Abstract
Giardiasis is among the ignored zoonotic illnesses accorded by the World Health Organization that is caused by Giardia lamblia. This study developed a mathematical model for giardiasis transmission that incorporates both sensitive and resistant strains of the parasite. The model, built as a system of nonlinear differential equations, captures host-to-host spread, environmental contamination, and strain interaction. Key thresholds, such as the basic reproduction numbers for each strain, are derived to determine conditions for disease persistence or eradication, local stability of the disease free was determined using the routh hurwitz criterion which shows that the model is locally and asymptotically stable when R0 < 1 and unstable if R0 >1 while the Castillo-Chavez and song method is used to show the overall adequacy of the global stability of the equilibrium point free from the disease and it satisfied that it is globally and asymptotically stable. In addition, a Lyapunov function was constructed to study the stability of the endemic equilibrium point and the model satisfied both conditions. Sensitivity analysis highlights parameters most influencing transmission, including contact, shedding, and treatment factors. Numerical simulations support the theoretical findings, showing how poor treatment or partial compliance can allow resistant strains to persist even when sensitive strains are controlled. Overall, the study provides a rigorous framework for understanding giardiasis dynamics and offers practical insights for improving treatment and public health interventions. The results offer valuable insights into the thresholds for eradication, the potential risks of drug resistance. We advised that medical treatment programs should be strengthened to increase the recovery rate of infected individuals especially those with the resistant strain, thereby reducing the infectious period. Public health interventions should focus on reducing
environmental contamination through improved sanitation, safe water supply, and hygiene promotion.
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