Document Type : Research Paper
Authors
1
School of Distance Education, Universiti Sains Malaysia, USM, 11800, Penang, Malaysia.
2
1) School of Distance Education, Universiti Sains Malaysia, USM, 11800, Penang, Malaysia. 2) School of Mathematical Sciences, Universiti Sains Malaysia, USM, 11800, Penang, Malaysia.
3
Department of Mathematics, University of Management and Technology, CII Johar Town, Lahore, 54770, Punjab, Pakistan.
4
School of Biological Sciences, Universiti Sains Malaysia, USM, 11800, Penang, Malaysia.
5
Department of Mathematics, Namal University 30km Talagang Road, Mianwali, 42250, Pakistan.
Abstract
Dengue fever is a viral illness affecting over 129 nations
and more than 50% of the global population, causing
approximately 400 million cases annually. This study
explores the mathematical formulation and dynamics of
dengue transmission using a structured SEIR-SEI
(susceptible human, exposed human, infected human,
recovered human, susceptible vector, exposed vector, and
infected vector) model, focusing on immunological and
delay-based control strategies. An existing nonlinear
delayed SEIR-SEI epidemic model is extended to evaluate
the effectiveness of awareness, mosquito deterrence, and
therapeutic interventions. Rather than immediately
resorting to pharmacological methods, the model emphasizes
on analyzing delay factors due to their significant role
in disease control. Since reducing mosquito populations
can harm ecological balance, this new approach applies
delay-based strategies on human-related factors such as
hospitalization, awareness, and travel restrictions to
safeguard both public health and the environment. The
findings show that the reproductive number alone is
insufficient to predict outbreak persistence; recruitment
patterns and mosquito biting rates play a more pivotal
role. We analyze the model's mathematical properties,
including the reproduction number, equilibrium points,
parameter sensitivity, and both local and global
stability. Our results demonstrate that model-based
strategies focusing on vector control and human behavior
effectively reduce dengue transmission. Additionally, we
show that the non-standard finite difference scheme
outperforms traditional methods like the fourth-order
Runge-Kutta in terms of accuracy, stability, and
predictive capability. This study offers valuable insights
for public health officials and policymakers in designing
sustainable strategies to control endemic dengue
transmission and prevent future outbreaks.
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