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Ebola Virus disease (EVD) is an emerging and re-emerging zoonotic disease which mostly occur in Africa. Both prediction of the next EVD and controlling an ongoing outbreak remain challenging to disease prone countries. Depending on previous experiences to curb an outbreak is subjective and often inadequate as temporal socioeconomic advances are dynamic and complex at each disease. We hypothesize that a scientific model would predict EVD disease outbreak control. In this work, a mathematical model with a convex incidence rate for an optimal control model of Ebola Virus Disease is formulated and analyzed. An optimal control strategy which aims at reducing the number of infected individuals in the population and increasing the number of recovered through treatment is evaluated. Three control measures: tracing of contacts, lock-down and treatment have been considered. A qualitative analysis and numerical experiments are performed on the model and the findings reveal that the most expensive strategy involved imposing lock-down and contact tracing of the infected while the cheapest alternative was lock-down and treatment of the infected. Hence, policy makers should concentrate on treatment and lock down to combat the disease.

Coronavirus disease 2019 (COVID-19) has dramatically spread all over the world, crossing the borders of all countries. It is presented mainly by lower respiratory tract symptoms such as fever, cough, dyspnea, and chest tightness. However, COVID-19 causes different upper respiratory tract-related symptoms including nasal congestion, sore throat, and olfactory dysfunction. Therefore, this study was aimed to evaluate the Prevalence and otorhinologic / Ear Nose and Throat ( ENT) Symptomatology of Individual with COVID-19 in Rivers State. The study was a prospective descriptive study of all consenting patients who received care through hospitals, designated for COVID-19 treatment in Rivers State. A total number of 2223 Samples consisting of 137 (6.16%) symptomatic and 2086 asymptomatic (93.84%) were taken in accordance with Nigerian protocol for samples collection and PCR Diagnosis for SARS COV-2. The age, sex, date onset of symptoms, and date of sample collection were documented. A diagnosis of COVID-19 infection was made according to the guidance developed by the NCDC using multiplex RT‑PCR which identified the E‑gene, RDRP‑gene, and N-gene using GeneFinder by Osang Korea. Results revealed that out of the total number of 2223 patients tested 206 were positive of COVID-19 and 2017 (91%) were tested negative. Out 206 positive cases recorded 110 patients were with symptoms, the most frequent recorded ENT manifestations were dry cough and fever (24.5%), loss of smell (24.5%), Difficulty in Breathing (11.8%),Headache (10.9%), Sore throat (7.3%), Nasal congestion (6.5%),,Loss of taste (6.4%),Sneezing (3.6%), dizziness (2.7%), and running nose (1.8%). The study has shown that the prevalence of COVID-19 among symptomatic and asymptomatic patients in the study location is high and a cause of epidemiologic concern as asymptomatic patients contribute a significant burden and carriers of COVID-19 infections. The study also revealed that ENT syndrome is the major symptoms associated with Covid 19.

In this study, we present a non-autonomous model with a Holling type II functional response, to study the complex dynamics for fall armyworm-maize biomass interacting in a periodic environment. Understanding how seasonal variations affect fall armyworm-maize dynamics is critical since maize is one of the most important cereals globally. Firstly, we study the dynamical behaviours of the basic model; that is, we investigate positive invariance, boundedness, permanence, global stability and non-persistence. We then extended the model to incorporate time dependent controls. We investigate the impact of reducing fall armyworm egg and larvae population, at minimal cost, through traditional methods and use of chemical insecticides. We noted that seasonal variations play a significant role on the patterns for all fall armyworm populations (egg, larvae, pupae and moth). We also noted that in all scenarios, the optimal control can greatly reduce the sizes of fall armyworm populations and in some scenarios, total elimination may be attained. The modeling approach presented here provides a framework for designing effective control strategies to manage the fall armyworm during outbreaks.

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

A deterministic mathematical model for brucellosis that incorporates seasonality on direct and indirect transmission parameters for domestic ruminants, wild animals, humans, and the environment was formulated and analyzed in this paper. Both analytical and numerical simulations are presented. From this study, the findings show that variations in seasonal weather have the great impact on the transmission dynamics of brucellosis in humans, livestock, and wild animals. Thus, in order for the disease to be controlled or eliminated, measures should be timely implemented upon the fluctuation in the transmission of the disease.

This research article published by the Journal of Mathematics and Informatics Vol. 19, 2020

In 2013 the World Health Organization recommended the initiation of antiretroviral therapy (ART) to any person who tests HIV positive irrespective of his/her CD4 + count. However, implementation of the new guidelines poses a lot of challenges especially in Sub-Sahara Africa such as: drug side effects, drug resistance-mutations and significant financial burdens. Most importantly, it has been established that HIV resistance and subsequent virologic failure occur in a substantial proportion of HIV-infected patients receiving HAART. This study therefore, seeks to investigate the emergence of drug resistant HIV virus during treatment with the aim of determining the proper use of HIV therapy that would lessen drug resistance. To carry out the analysis a ten dimensional in-vivo mathematical model is proposed for HIV dynamics. The model is formulated in such away that it takes into account two virus strain, that is, the wild type as well as the naive type HIV virus. The in-vivo model is shown to be both biologically meaningful and mathematically well posed. The existence of unique infection-free equilibrium point is determined and both its local and global stability investigated. In addition, the basic reproduction number for each viral strain is computed using the next generation matrix method. An optimal control model is proposed and analysed by applying Pontryagin maximum principle, to obtain the optimal drug combination for HIV treatment. Here two drugs, that is, Reverse Transcriptase inhibitor and Protease inhibitor are used as the controls in the model. We provide an objective function for the minimisation of the number of wild type HIV virus and the drug resistant virus as well as the costs associated with the use of Reverse Transcriptase inhibitor and protease inhibitor. The forward backward sweep method is applied to numerically solve the optimality system. From the numerical simulations, it is evident that protease inhibitor is the most effective drug in controlling HIV infection. The results suggest that prolonged use of HAART leads to development of drug resistant and that people with drug-resistant infection could play a core role in the epidemic of HIV.