Numerical Scheme for Compartmental Models: New Matlab Software Codes for Numerical Simulation.

Background: This paper presents a newly developed Matlab code for the numerical simulation of compartmental/deterministic models. It addresses modeling and simulation issues concerning compartmental models. The code is easy to understand and edit for the simulation of compartmental models. An alternative codes for statistical software package R has been proposed for the same model. R software is freely available for use. Methods: We proposed a basic SEIR model for illustration purposes. Matlab and R software codes are developed for the SEIR model which users can follow and easily understand the computations. Results: The two codes work on all Matlab and R versions. For models with more compartments, we suggest using higher version of Matlab and R. Matlab works on windows, Mac and Linux Conclusions: New Matlab software codes purposely for numerical simulations of classical deterministic models which can run on any version of Matlab has been introduced in this paper. This code can be edited/modify to suit any deterministic models and any desired output required. An alternative open source free version has been written in R has been provided as well.

Modeling and analysis of monkeypox disease using fractional derivatives.

The frequency of monkeypox outbreaks and the extent of the projected outbreaks in human populations have both steadily increased. This paper proposes Atangana-Baleanu fractional-order derivatives define in Caputo sense to investigate the kinetics of Monkeypox transmission in Ghana. We determine the stability of the recommended model's equilibrium points and basic reproduction number. The solution's existence and originality, as well as the model's Hyers-Ullam stability, are proven. The models basic reproduction number was found to be R 0 = 0.1940. The numerical simulation showed the fractional operator had an influence on the various compartments of the model. The dynamics of the disease in the community were shown to be influenced by fractional-order derivatives, and infections were eradicated within the first five (5) days when π = 0.2.

Fractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate.

Coinfection of Ebola virus and malaria is widespread, particularly in impoverished areas where malaria is already ubiquitous. Epidemics of Ebola virus disease arise on a sporadic basis in African nations with a high malaria burden. An observational study discovered that patients in Sierra Leone's Ebola treatment centers were routinely infected with malaria parasites, increasing the risk of death. In this paper, we study Ebola-malaria coinfections under the generalized Mittag-Leffler kernel fractional derivative. The Banach fixed point theorem and the Krasnoselskii type are used to analyse the model's existence and uniqueness. We discuss the model stability using the Hyers-Ulam functional analysis. The numerical scheme for the Ebola-malaria coinfections using Lagrange interpolation is presented. The numerical trajectories show that the prevalence of Ebola-malaria coinfections ranged from low to moderate depending on memory. This means that controlling the disease requires adequate knowledge of the past history of the dynamics of both malaria and Ebola. The graphical dynamics of the detection rate indicate that a variation in the detection rate only affects the following compartments: individuals that are latently infected with the Ebola, Ebola virus afflicted people who went unnoticed, individuals who have been infected with the Ebola virus and have been diagnosed with the disease, and persons undergoing Ebola virus therapy.

Mathematical modelling of the epidemiology of COVID-19 infection in Ghana.

In this paper, Covid-19 patients with self-immunity is incorporated in the Susceptible-Exposed-Infected-Quarantined-Recovered ( S E I Q R ) model is applied to describe the epidemiology of Covid-19 infection in Ghana. Based on data on the epidemiology of the Covid-19 infection in Ghana, we observed that, on an average, three persons contract the Covid-19 infection from an infected person daily based using the basic reproductive number ( R o ) derived from the SEIQR model. In addition, the threshold condition for the long term stability of the Covid-19 infection in Ghana is derived from this model. Based on the Dulac criterion, it was observed that for a long period of time the epidemiology of Covid-19 in Ghana will be under control. Again, we observed that both the transmission rate natural death rate of a person in the various classes mostly influence the spread of Covid-19 infection followed by the exposed rate from exposure class to the infected class, then the rate at which an infected person is quarantined and finally, the rate at an exposed person is quarantined. On the other hand, the rate at which an exposed person recovers from his/her have least influence on the spread of Covid-19 infection in the country. Nevertheless, the rates of birth, transmission of Covid-19 infection to a susceptible person, exposure to Covid-19 infection and Covid-19 patient who is quarantined by the facilities provided by the Ghana Health Service ( G H S ) are in direct relationship with R o . However, the rates at which a quarantiner dies from a Covid-19 infection, an infected person dies from a Covid-19 infection, natural death from each class and the recoveries from an infected class, exposed class and quarantined class are in relationship with R o .