Mathematical Modelling of Transmission Dynamics of Anthrax in Human and Animal Population.

Anthrax is an infectious disease that can be categorised under zoonotic diseases. It is caused by the bacteria known as Bacillus anthraces. Anthrax is one of the most leading causes of deaths in domestic and wild animals. In this paper, we develop and investigated a mathematical model for the transmission dynamics of the disease. Ordinary differential equations were formulated from the mathematical model. We performed the quantitative and qualitative analysis of the model to explain the transmission dynamics of the anthrax disease. We analysed and determined the model’s steady states solutions. The disease-free equilibrium of the anthrax model is analysed for locally asymptotic stability and the associated epidemic basic reproduction number. The model’s disease free equilibrium has shown to be locally asymptotically stable when the basic reproductive number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Sensitivity analysis was performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the diseases. Keywords: Anthrax model, Basic reproductive number, Asymptotic stability, Endemic equilibrium, Sensitivity analysis

An Optimal Treatment Control of TB-HIV Coinfection

An optimal control on the treatment of the transmission of tuberculosis-HIV coinfection model is proposed in this paper. We use two treatments, that is, anti-TB and antiretroviral, to control the spread of TB and HIV infections, respectively. We first present an uncontrolled TB-HIV coinfection model. The model exhibits four equilibria, namely, the disease-free, the HIV-free, the TB-free, and the coinfection equilibria. We further obtain two basic reproduction ratios corresponding to TB and HIV infections. These ratios determine the existence and stability of the equilibria of the model. The optimal control theory is then derived analytically by applying the Pontryagin Maximum Principle. The optimality system is performed numerically to illustrate the effectiveness of the treatments

Severity of imported malaria: protective effect of taking malaria chemoprophylaxis

BACKGROUND: Although chemoprophylaxis remains an important strategy for preventing malaria in travellers, its effectiveness may be compromised by lack of adherence. Inappropriate use of chemoprophylaxis is likely to increase the risk of acquiring malaria, but may probably also worsen the severity of imported cases. The aim of this study was to assess the impact of use of malaria chemoprophylaxis on clinical features and outcome of imported malaria. METHODS: Demographic, clinical and laboratory data of patients included in the Rotterdam Malaria Cohort between 1998 and 2011 were systematically collected and analysed. Patients were classified as self-reported compliant or non-compliant users or as non-users of chemoprophylaxis. Severe malaria was defined using the 2010 WHO criteria. RESULTS: Details on chemoprophylaxis were available for 559 of the 604 patients, of which 64.6% were non-users, 17.9% were inadequate users and 17.5% reported to be adequate users. The group of non-users was predominated by patients with African ethnicity, partial immunity and people visiting friends and relatives. The majority contracted Plasmodium falciparum malaria. In contrast, compliant users acquired non-falciparum malaria more frequently, had significant lower P. falciparum loads on admission, shorter duration of hospitalization and significant lower odds for severe malaria as compared with non-users. Patients with P. falciparum malaria were more likely to have taken their chemoprophylaxis less compliantly than those infected with non-P. falciparum species. Multivariate analysis showed that self-reported adequate prophylaxis and being a partially immune traveller visiting friends and relatives was associated with significantly lower odds ratio of severe malaria. In contrast, age, acquisition of malaria in West-Africa and being a non-immune tourist increased their risk significantly. CONCLUSIONS: Compliant use of malaria chemoprophylaxis was associated with significantly lower odds ratios for severe malaria as compared with non-compliant users and non-users of chemoprophylaxis. After correction for age, gender and immunity, this protective effect of malaria chemoprophylaxis was present only in individuals who adhered compliantly to use of chemoprophylaxis. Patients with P. falciparum malaria were more likely to have used their chemoprophylaxis less compliantly than patients with non-P. falciparum malaria who were more likely to have contracted malaria in spite of compliant use of chemoprophylaxis

Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi

Malaria is a public health problem for more than 2 billion people globally. About 219 million cases of malaria occur worldwide and 660,000 people die, mostly (91%) in the African Region despite decades of efforts to control the disease. Although the disease is preventable, it is life-threatening and parasitically transmitted by the bite of the female Anopheles mosquito. A deterministic mathematical model with intervention strategies is developed in order to investigate the effectiveness and optimal control strategies of indoor residual spraying (IRS), insecticide treated nets (ITNs) and treatment on the transmission dynamics of malaria in Karonga District, Malawi. The effective reproduction number is analytically computed, and the existence and stability conditions of the equilibria are explored. The model does not exhibit backward bifurcation. Pontryagin’s Maximum Principle which uses both the Lagrangian and Hamiltonian principles with respect to a time dependent constant is used to derive the necessary conditions for the optimal control of the disease. Numerical simulations indicate that the prevention strategies lead to the reduction of both the mosquito population and infected human individuals. Effective treatment consolidates the prevention strategies. Thus, malaria can be eradicated in Karonga District by concurrently applying vector control via ITNs and IRS complemented with timely treatment of infected people

Mathematical modeling and analysis of HIV/AIDS control measures

>Magister Scientiae - MScIn this thesis, we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyse a math- ematical model that describes the dynamics of HIV infection among the im- migrant youths and intervention that can minimize or prevent the spread of the disease in the population. In particular, we are interested in the effects of public-health education and of parental care.We consider existing models of public-health education in HIV/AIDS epidemi-ology, and provide some new insights on these. In this regard we focus atten-tion on the papers [b] and [c], expanding those researches by adding sensitivity analysis and optimal control problems with their solutions.Our main emphasis will be on the effect of parental care on HIV/AIDS epidemi-ology. In this regard we introduce a new model. Firstly, we analyse the model without parental care and investigate its stability and sensitivity behaviour.We conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is asymptotically stable. Further, we use optimal control methods to determine the necessary conditions for the optimality of intervention, and for disease eradication or control. Using Pontryagin’s Maximum Principle to check the effects of screening control and parental care on the spread of HIV/AIDS, we observe that parental care is more effective than screening control. However, the most efficient control strategy is in fact a combination of parental care and screening control. The results form the central theme of this thesis, and are included in the manuscript [a] which is now being reviewed for publication. Finally, numerical simulations are performed to illustrate the analytical results

A mathematical model for coinfection of listeriosis and anthrax diseases

CITATION: Osman, S. & Makinde, O. D. 2018. A mathematical model for coinfection of listeriosis and anthrax diseases. International Journal of Mathematics and Mathematical Sciences, 2018 (Article ID 1725671), doi:10.1155/2018/1725671.The original publication is available at https://www.hindawi.comListeriosis and Anthrax are fatal zoonotic diseases caused by Listeria monocytogene and Bacillus Anthracis, respectively. In this paper, we proposed and analysed a compartmental Listeriosis-Anthrax coinfection model describing the transmission dynamics of Listeriosis and Anthrax epidemic in human population using the stability theory of differential equations. Our model revealed that the disease-free equilibrium of the Anthrax model only is locally stable when the basic reproduction number is less than one. Sensitivity analysis was carried out on the model parameters in order to determine their impact on the disease dynamics. Numerical simulation of the coinfection model was carried out and the results are displayed graphically and discussed. We simulate the Listeriosis-Anthrax coinfection model by varying the human contact rate to see its effects on infected Anthrax population, infected Listeriosis population, and Listeriosis-Anthrax coinfected population.https://www.hindawi.com/journals/ijmms/2018/1725671/Publisher's versio

Chagas Disease in the United States: a Public Health Approach.

Trypanosoma cruzi is the etiological agent of Chagas disease, usually transmitted by triatomine vectors. An estimated 20 to 30% of infected individuals develop potentially lethal cardiac or gastrointestinal disease. Sylvatic transmission cycles exist in the southern United States, involving 11 triatomine vector species and infected mammals such as rodents, opossums, and dogs. Nevertheless, imported chronic T. cruzi infections in migrants from Latin America vastly outnumber locally acquired human cases. Benznidazole is now FDA approved, and clinical and public health efforts are under way by researchers and health departments in a number of states. Making progress will require efforts to improve awareness among providers and patients, data on diagnostic test performance and expanded availability of confirmatory testing, and evidence-based strategies to improve access to appropriate management of Chagas disease in the United States

Optimal (control of) intervention strategies for malaria epidemic in Karonga district, Malawi

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. December 2, 2014.Malaria is a public health problem for more than 2 billion people globally. About 219 million cases of malaria occur worldwide and 660, 000 people die, most (91%) in the African region despite decades of efforts to control the disease. Although the disease is preventable, it is life-threatening and parasitically transmitted by the bite of the female Anopheles mosquito. A deterministic mathematical model with intervention strategies is developed in order to investigate the effectiveness, optimal control and cost effectiveness of Indoor Residual Spraying (IRS), Insecticide Treated Nets (ITNs) and treatment on the transmission dynamics of malaria in Karonga District, Malawi. The effective reproduction number is analytically computed, and existence and stability conditions of the equilibria are explored. The model does not exhibit backward bifurcation. A structured questionnaire was developed, a one-toone interview with a randomly sampled set of individuals conducted to assess the knowledge level of inhabitants of Karonga district about the disease in general and their awareness and application of the intervention strategies. Applying Pontryagin’s Maximum Principle which uses both the Langragian and Hamiltonian principles with respect to a constant time dependent, we derive the necessary conditions for the optimal control of the disease. An economic evaluation of the strategies is carried out by performing a cost-effectiveness analysis to determine the most cost-effective combination of the three intervention measures. The incremental cost-effectiveness ratio (ICER) is calculated in order to compare the costs and effectiveness of all the possible combinations of the three measures. The results show that the combination of treatment, ITNs and IRS is the most cost-effective combination strategy for malaria control. Numerical simulations indicate that the prevention strategies lead to the reduction of both the mosquito population and infected human individuals. Effective treatment consolidates the prevention strategies. Thus, malaria can be eradicated by deployment of combined strategies such as vector control via ITNs and IRS complemented with timely treatment of infected people

Elimination of Infectious Diseases from the South-East Asia Region

This book discusses the historical context, country experience, and best practices that led to eliminating infectious diseases from the WHO’s South-East Asia Region, such as malaria, lymphatic filariasis, yaws, trachoma, and mother-to-child HIV in the mid-twentieth and twenty-first century. The UN Sustainable Development Goals (3.3) targets to end AIDS, tuberculosis, malaria, and neglected tropical diseases and combat hepatitis, water-borne diseases and other communicable diseases by 2030. In this context, this book is of high significance to countries from the SEA region and around the globe. It helps create national strategies and action plans on infectious disease elimination and thus attaining SDG 3.3. This is an open access book