id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6775	Leo Amalraj, J. Leo ; Shukla, Pankaj ; Maguluri, Lakshmana Phaneendra ; Donganont, Siriluk; Avinash, N.; Govindan, Vediyappan	Backward Bifurcation and Optimal Control in an Age-Structured SVI Epidemic Model	2025	32	.pdf	application/pdf	12904	815	66	Math, 18 (4) (2025), 6775 27 of 32 Figure 5: Optimal treatment control α(t, x) at infection ages x = 0, 10, 20 for the age-structured SVI model (system (1)), comparing Scenario 1 (equal costs, solid lines) and Scenario 2 (higher treatment cost, dashed lines). According to the arithmetic–geometric mean inequality, both terms 2 − S S0 − S0 S and 3 − V V 0 − S0 S − S S0 V 0 V are nonnegative and the equality holds if and only if S = S0 and V = V 0.	cache/ejpam-6775.pdf	txt/ejpam-6775.txt