On the application of optimal control strategies to a generalized SVIR model

Abstract

In this paper, a deterministic optimal control problem involving a Susceptible - Vaccinated - Infected - Recovered (SVIR) epidemic model is considered. The optimal control problem is characterized using the Pontryagin’s maximum principle involving three control strategies namely, social mobilization, screening and sanitation. The derived optimality system is numerically solved using the forward - backward Runge - Kutta fourth order method via the computational software matlab. The numerical simulations depict that each of the control strategy has its significance in minimizing the spread of diseases, but the optimal combination of these controls are more effective in stemming the emergence and spread of an epidemic.

Bifurcation, sensitivity, and optimal control analysis of onchocerciasis disease transmission model with two groups of infectives and saturated treatment function

“…36 Many works have been done in applying different control interventions to stop the spread of several human, animal, and crop diseases. Some authors who have worked on the incorporation of optimal controls to a generalized real-world diseases and its management include previous studies, [37][38][39][40][41][42][43][44] while numerical techniques like the shooting method, finite difference scheme, and forward-backward Runge-Kutta scheme used in the solution of optimal control problems can be seen in previous studies. [45][46][47][48][49][50][51][52][53][54][55][56][57][58] In view of the earlier studies, several works done on the modeling of onchocerciasis only considered microsimulation and deterministic models and the impact of ivermectin drug treatment only as a control in eradicating the disease annually or bi-annually.…”

“…Many works have been done in applying different control interventions to stop the spread of several human, animal, and crop diseases. Some authors who have worked on the incorporation of optimal controls to a generalized real‐world diseases and its management include previous studies, 37–44 while numerical techniques like the shooting method, finite difference scheme, and forward–backward Runge–Kutta scheme used in the solution of optimal control problems can be seen in previous studies 45–58 …”