Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2202.06413

An Optimal Control Model of transmission dynamics of COVID-19 in Ghana

Samuel Okyere·Joseph Ackora-Prah·Ebenezer Bonyah·Kwaku Forkuoh Darkwah
View original source ↗Read source document ↗Export metadata ↓

Abstract

Almost every country in the world is battling to limit the spread of COVID-19. As the world strives to get an effective medication to control the disease, appropriate intervention measures, for now, remains one of the effective methods to reduce the spread of the disease. Optimal control strategies have proven to be an effective method in curtailing the spread of infectious diseases. In this paper, a model has been formulated to study transmission dynamics of the disease. Basic properties of the model such as the basic reproduction number, equilibrium points and stability of the equilibrium points have been determined. Sensitivity analysis was carried on to determine the impact of the model parameters on the basic reproduction number. We also introduced a compartment for the deceased and examined the behaviour of COVID-19 related deaths. The numerical simulation prediction is consistent with real data from Ghana for the period March 2020 to March 2021. The simulation revealed the disease had less impact on the population during the first seven months of the outbreak. To help contain the spread of the disease, time dependent optimal controls were incorporated into the model and Pontryagin maximum principle was used to characterize vital conditions of the optimal control model. Numerical simulations of the optimal control model showed that, combination of optimal preventive strategies such as nose mask and vaccination are effective to significantly decrease the number of COVID-19 cases in different compartments of the model. Vaccination decreases the susceptibility to the disease whereas mask usage preserved the susceptible population from extinction.

Explore related subjects

q-bio.PE

Keep this discovery

BibTeXRIS

Samuel Okyere, Joseph Ackora-Prah, Ebenezer Bonyah, Kwaku Forkuoh Darkwah. 2022-01-26. An Optimal Control Model of transmission dynamics of COVID-19 in Ghana. https://arxiv.org/abs/2202.06413

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Competition drives excessive recruitment in collective search

Groups that search collectively often exploit what they find by recruiting: one member directs others to a site it has found. Recruitment raises the number of members foraging at a known site, but the return per forager may fall as that number grows, so there is an intermediate optimal recruitment rate. In addition, a site may be used by more than one group. Here we analyze a model of two groups that forage from a single site whose return declines with the total number of foragers present. The two groups interact only through this shared return. The long-run outcome is either coexistence at the foraging site or monopoly by one group, and we analyze the boundary between these two outcomes. A group's best response to its rival is not monotone: it increases its own recruitment rate with the rival's recruitment rate in an attempt to preserve a monopoly, and then its recruitment rate drops discontinuously when it is no longer optimal to preserve a monopoly. We analyze how model parameters govern this shift: a group relinquishes monopoly when the site saturates at few foragers and when the rival group is small. When the two groups have comparable size there are multiple Nash equilibria, so either group may end up with the larger share. And when two equally matched groups compete, both recruit above the rate that maximizes their common return, so that each individual ends with less than it would in a single undivided group of the same total size.

q-bio.PE↗
arXiv2026

Selection Rules for Species Coexistence in a Hierarchical May-Leonard Model

One of the central challenges in evolutionary dynamics is understanding why some species combinations persist while others disappear. Although cyclic-interaction models have provided fundamental insights into biodiversity maintenance, much less is known about how hierarchical competitive interactions shape long-term community organization. Here, we investigate a hierarchical extension of the May-Leonard model, in which species interact through a directed predation chain while undergoing reproduction and mortality. Combining mean-field analysis with Monte Carlo simulations, we show that the fully coexisting state is generically unstable, causing the dynamics to evolve toward lower-dimensional coexistence states. The simulations further reveal stochastic extinctions dominating small populations with the dynamics progressively approaching the mean-field predictions as the system size increases. Rather than permitting arbitrary species combinations, the hierarchical-interaction structure dynamically constrains coexistence by selecting only specific subsets of species for long-term persistence. We show that these admissible coexistence states have a natural graph-theoretic interpretation as independent sets in the hierarchical interaction network, thereby providing general constraints on coexistence in hierarchical communities. Together, these results establish a theoretical framework linking hierarchical interactions, dynamical selection, graph topology, and biodiversity organization, extending the classical May-Leonard model beyond cyclic competition.

q-bio.PE↗
arXiv2026

Persistence of n-Species Lotka-Volterra Models with Periodic Pulses

Periodic impulsive interventions arise naturally in the management of biological populations, including chemotherapy, pesticide application, and infectious-disease treatment. We develop general conditions for permanence in n-species population models subject to periodic multiplicative pulse disturbances. Our main result provides a sufficient condition for permanence in terms of weighted long-term growth rates on a Morse decomposition of the extinction set, explicitly separating the contributions of continuous population dynamics from those of the periodic pulse. To establish this result, we transform the impulsive system into an associated autonomous continuous-time dynamical system and use this correspondence to extend classical permanence theory to periodically pulsed models. We further show that the same conditions imply robust permanence under sufficiently small perturbations to the continuous dynamics, pulse period, and pulse effects. We illustrate the framework with two Lotka-Volterra models motivated by biological control: competition between chemotherapy-sensitive and chemotherapy-resistant cancer cells, and integrated control of an agricultural pest using pesticides and parasitoids. These examples demonstrate how intervention frequency and intensity interact with underlying ecological interactions to determine whether populations coexist or are excluded. Our results provide a general framework for analyzing persistence in ecological systems subject to repeated discrete disturbances.

q-bio.PE↗