Dog screening as a novel complementary guinea worm disease control tool to mitigate persistence in Chad: A modeling study.

A free-roaming dog population remains one of the major public health problems in many developing countries. In this study, we investigated the potential impact of owned roaming and stray dogs on the persistence and possible eradication of Guinea worm disease (GWD) in Chad. We developed and analysed a multi-host of Guinea worm; and considered dogs as the definitive hosts, and fish as the intermediate hosts. Currently, GWD cases in the human population are low; hence, we ignored the human population in this study. We derived the reproduction number and explored how it depends on different model parameters that define it. We calibrated the proposed model with data from literature and validated it with recently reported GWD monthly data for dog infection in Chad from 2019 to 2022. Results show that detection and tethering of infectious owned free-roaming dogs combined with culling of stray dogs are effective disease management strategies. Hence, attainment of certain threshold levels for these interventions could lead to disease eradication. Overall, the study revealed how different factors could be applied to effectively manage GWD transmission in the dog population. Findings from this study could be used to support decision-making in GWD control strategies. Mathematics Subject Classification (2010): 92B05, 93A30, 93C15.

Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class.

In this paper, a nonlinear fractional-order chikungunya disease model that incorporates asymptomatic infectious individuals is proposed and analyzed. The main interest of this work is to investigate the role of memory effects on the dynamics of chikungunya. Qualitative analysis of the model's equilibria showed that there exists a threshold quantity which governs persistence and extinction of the disease. Model parameters were estimated based on the 2015 weekly reported cases in Colombia. The Adams-Bashforth-Moulton method was used to numerically solve the proposed model. We investigated the role of asymptomatic infectious patients on short- and long-term dynamics of the diseases. We also determined threshold levels for the efficacy of preventative strategies that results in effective management of the disease. We believe that our model can provide invaluable insights for public health authorities to predict the effect of chikungunya transmission and analyze its underlying factors and to guide new control efforts.

On the role of governmental action and individual reaction on COVID-19 dynamics in South Africa: A mathematical modelling study.

Mathematical models proffer a rational basis to epidemiologists and policy makers on how, where and when to control an infectious disease. Through mathematical models one can explore and provide solutions to phenomena which are difficult to measure in the field. In this paper, a mathematical model has been used to explore the role of government and individuals reaction to the recent outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The proposed framework incorporates all the relevant biological factors as well as the effects of individual behavioral reaction and government action such as travel restrictions, social distancing, hospitalization, quarantine and hygiene measures. Understanding the dynamics of this highly contagious SARS-CoV-2, which at present does not have any therapy assist the policy makers on evaluating the effectiveness of the control measures currently being implemented. Moreover, policy makers can have insights on short-and-long term dynamics of the disease. The proposed conceptual framework was combined with data on cases of coronavirus disease (COVID-19) in South Africa, March 2020 to early May 2020. Overall, our work demonstrated optimal conditions necessary for the infection to die out as well as persist.

Dynamical and optimal control analysis of a seasonal Trypanosoma brucei rhodesiense model.

The effects of seasonal variations on the epidemiology of Trypanosoma brucei rhodesiense disease is well documented. In particular, seasonal variations alter vector development rates and behaviour, thereby influencing the transmission dynamics of the disease. In this paper, a mathematical model for Trypanosoma brucei rhodesiense disease that incorporates seasonal effects is presented. Owing to the importance of understanding the effective ways of managing the spread of the disease, the impact of time dependent intervention strategies has been investigated. Two controls representing human awareness campaigns and insecticides use have been incorporated into the model. The main goal of introducing these controls is to minimize the number of infected host population at low implementation costs. Although insecticides usage is associated with adverse effects to the environment, in this study we have observed that by totally neglecting insecticide use, effective disease management may present a formidable challenge. However, if human awareness is combined with low insecticide usage then the disease can be effectively managed.

Optimal control applied to a temperature dependent schistosomiasis model.

Schistosomiasis, the most common water-borne infection worldwide, continues to pose a serious public health challenge in developing nations and to travellers who visit these endemic regions. We apply optimal control on a temperature dependent schistosomiasis model. Our optimal control aims to minimize the pre-patent and patent human population at minimal costs. Our analysis and results throughout the paper highlight the impact of optimal control shaping the future patterns of the disease. Our results show that optimal control can significantly reduce the schistosomiasis burden in the community and in some instance by more than three-fold. In addition, our results show that with low costs the optimal strategy will be carried out at or close to its maximum strength for a sufficiently long period of time, so as minimize the exposure and infection. With high costs, however, the control have to be implemented with reduced or even minimum, strength, to achieve an optimal balance between the costs and effects of control. Our findings suggest that optimal control theory can be useful on minimizing the infected host and vector. The study and its findings can provide a useful framework for designing cost-effective control for schistosomiasis.

On the dynamics of brucellosis infection in bison population with vertical transmission and culling.

We introduce a new mathematical modeling framework that seek to improve our quantitative understanding of the influence of chronic brucellosis and culling control on brucellosis dynamics in periodic and non-periodic environments. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. In addition, we also perform an optimal control study to explore optimal culling strategy in periodic and non-periodic environment.

Modeling the intrinsic dynamics of foot-and-mouth disease.

We propose a new mathematical modeling framework to investigate the transmission and spread of foot-and-mouth disease. Our models incorporate relevant biological and ecological factors, vaccination effects, and seasonal impacts during the complex interaction among susceptible, vaccinated, exposed, infected, carrier, and recovered animals. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. In addition, numerical simulation results are presented to demonstrate the analytical findings.

Modeling the Effects of Multiple Intervention Strategies on Controlling Foot-and-Mouth Disease.

Foot-and-mouth disease (FMD) is a threat to economic security and infrastructure as well as animal health, in both developed and developing countries. We propose and analyze an optimal control problem where the control system is a mathematical model for FMD that incorporates vaccination and culling of infectious animals. The control functions represent the fraction of animals that are vaccinated during an outbreak, infectious symptomatic animals that are detected and culled, and infectious nonsymptomatic animals that are detected and culled. Our aim was to study how these control measures should be implemented for a certain time period, in order to reduce or eliminate FMD in the community, while minimizing the interventions implementation costs. A cost-effectiveness analysis is carried out, to compare the application of each one of the control measures, separately or in combination.

Modeling Illicit Drug Use Dynamics and Its Optimal Control Analysis.

The global burden of death and disability attributable to illicit drug use, remains a significant threat to public health for both developed and developing nations. This paper presents a new mathematical modeling framework to investigate the effects of illicit drug use in the community. In our model the transmission process is captured as a social "contact" process between the susceptible individuals and illicit drug users. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. Using our model, we present illustrative numerical results with a case study in Cape Town, Gauteng, Mpumalanga and Durban communities of South Africa. In addition, the basic model is extended to incorporate time dependent intervention strategies.

Mathematical modelling of immune regulation of type 1 diabetes.

Type 1 diabetes is a disease characterized by progressive loss of ß cell function due to an autoimmune reaction affecting the islets of Langerhans. Two types of T cells are involved in diabetes: turncoat auto-reactive T cells, or T cells gone bad, that kill the insulin-producing cells, and regulatory T cells that are unable to control the auto-reactive T cells. We formulate a mathematical model that incorporates the role of cytotoxic T cells and regulatory T cells in type 1 diabetes. This study shows that onset of type 1 diabetes is due to a collective, dynamical instability, rather than being caused by a single etiological factor. It is also a numbers game between regulatory T cells and auto-reactive T cells. The problem in the onset of this disease is that there are not enough of the regulatory cells that suppress the immune response against the body's insulin-producing pancreatic islet cells.

Modelling the effects of condom use and antiretroviral therapy in controlling HIV/AIDS among heterosexuals, homosexuals and bisexuals.

A deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals in heterosexual settings in which homosexuality and bisexuality issues have remained taboo is presented. We extend the model to focus on the effects of condom use as a single strategy approach in HIV prevention in the absence of any other intervention strategies. Initially, we model the use of male condoms, followed by incorporating the use of both the female and male condoms. The model includes two primary factors in condom use to control HIV which are condom efficacy and compliance. Reproductive numbers for these models are computed and compared to assess the effectiveness of male and female condom use in a community. We also extend the basic model to consider the effects of antiretroviral therapy as a single strategy. The results from the study show that condoms can reduce the number of secondary infectives and thus can slow the development of the HIV/AIDS epidemic. Further, we note from the study that treatment of AIDS patients may enlarge the epidemic when the treatment drugs are not 100% effective and when treated AIDS patients indulge in risky sexual behaviour. Thus, the treatment with amelioration of AIDS patients should be accompanied with intense public health educational programs, which are capable of changing the attitude of treated AIDS patients towards safe sex. It is also shown from the study that the use of condoms in settings with the treatment may help in reducing the number of secondary infections thus slowing the epidemic.