AGE-STRUCTURED MODEL WITH DELAY FOR THE STUDY OF SCHISTOSOMIASE IN NIGER
Keywords:
SEIRS model, age-structured, delay, nonlinear integro-differential system, stability, SchistosomiaseDOI:
https://doi.org/10.17654/0975045225015Abstract
In this paper, an age-structured model with delay applied to Schistosomiase in the Republic of Niger is studied. First, the model is formulated using delay differential equations [25]. Then, the basic reproduction number is determined. Once this task is completed, the stability of the disease-free equilibrium point is analyzed. The analytical and numerical results obtained show the stability of the disease-free equilibrium point. Subsequently, by substitution, the endemic equilibrium point is determined. Then, its stability is investigated by using the method of Routh Hurwitz [5, 23, 25]. To do this, the dynamic system reflecting the dynamics of the disease is linearized. Then, the characteristic polynomial of the linearized system is determined. A polynomial depending on the incubation time of the disease is obtained [22, 25]. Afterwards, the stability of the equilibrium point depending on the value of the incubation time is discussed. The analytical and numerical results obtained show that the endemic equilibrium point is stable when the time delay is neglected and it is unstable from certain values of the incubation time. From the analytical and simulation results, we observed that a Hopf bifurcation occurs for a certain value of latency time.
Received: March 18, 2025
Revised: April 24, 2025
Accepted: April 30, 2025
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