It is well established that people with diabetes are more likely to have serious complications from COVID-19. Nearly 1 in 5 COVID-19 deaths in the African region are linked to diabetes. World Health Organization (WHO) finds that 18.3% of COVID-19 deaths in Africa are among people with diabetes. In this paper, we have formulated and analysed a mathematical comorbidity model of diabetes-COVID-19 of the deterministic type. The basic properties of the model were explored. The basic reproductive number, equilibrium points, and stability of the equilibrium points were examined. Sensitivity analysis of the model was carried on to determine the impact of the model parameters on the basic reproductive number R 0 of the model. The model had a unique endemic equilibrium point, which was stable for R 0 > 1 . Time-dependent optimal controls were incorporated into the model with the sole aim of determining the best strategy for curtailing the spread of the disease. COVID-19 cases from March to September 2020 in Ghana were used to validate the model. Results of the numerical simulation suggest a greater number of individuals deceased when the infected individual had an underlying condition of diabetes. More so, the disease is endemic in Ghana with the basic reproduction number found to be R 0 = 1.4722 . The numerical simulation of the optimal control model reveals the lockdown control minimized the rate of decay of the susceptible individuals whereas the vaccination led to a number of susceptible individuals becoming immune to COVID-19 infections. In all, the two preventive control measures were both effective in curbing the spread of the disease as the number of COVID-19 infections was greatly reduced. We conclude that more attention should be paid to COVID-19 patients with an underlying condition of diabetes as the probability of death in this population was significantly higher.

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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 Ebolamalaria coinfections using Lagrange interpolation is presented. The numerical trajectories show that the prevalence of Ebolamalaria 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.

Given a list of real numbers      , we determine the conditions under which  will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute the elements of the matrix is derived for a given list and dependency parameters. Explicit computations are performed for  5 n  and to illustrate the result.

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