Mathematical modelling of Hepatitis E Virus (HEV) and Chronic Myeloid Leukemia (CML) co-infection dynamics

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.There are major advances which have been made to understand HEV and CML transmission dynamics but none of these have considered the effects of transmission parameters on the burden of HEV on CML prevalence in a co-infection scenario. We formulated a mathematical model for the co-infection of HEV and CML using a system of ordinary differential equations, in order to understand the effects of the co-infection on HEV and CML and vice versa in a human population. The model was analysed and steady state conditions were derived. Our results showed that the disease free equilibrium was both locally stable and globally stable if the basic reproduction number, R0 1. Our results also suggest that, (i) HEV reduces the CML infectives and accelerates the coinfection, (ii) CML enhances the progression of both HEV infection and the co-infection and, (iii) there is an increase in HEV-CML burden due to co-infection compared to single infections of either HEV or CML

Mathematical modelling of Hepatitis E Virus (HEV) and Chronic Myeloid Leukemia (CML) co-infection dynamics

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.There are major advances which have been made to understand HEV and CML transmission dynamics but none of these have considered the effects of transmission parameters on the burden of HEV on CML prevalence in a co-infection scenario. In this paper we formulated a mathematical model for the co-infection of HEV and CML using a system of ordinary differential equations, in order to understand the effects of the co-infection on HEV and CML and vice versa in a human population. The model was analysed and steady state conditions were derived. Our results showed that the disease free equilibrium was both locally stable and globally stable if the basic reproduction number, R0 ≤ 1 and unstable if the basic reproduction number, R0 > 1. Our results also suggest that, (i) HEV reduces the CML infectives and accelerates the co-infection, (ii) CML enhances the progression of both HEV infection and the co-infection and, (iii) there is an increase in HEV-CML burden due to coinfection compared to single infections of either HEV or CML.Mbarara University of Science and Technology, Mbarara, Kwa-Zulu University, Natal, South Afric

Multipatch Stochastic Epidemic Model for the Dynamics of a Tick-Borne Disease

Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the largest patch reproduction number and for connected patches it lies between the minimum and maximum of the patch reproduction numbers. Numerical simulations for a two-patch deterministic and stochastic differential equation models are performed to illustrate the dynamics of the disease for varying migration rates. Our results show that the probability of eliminating or minimizing the disease in both patches is high when there is no migration unlike when it is present. The results imply that the probability of disease extinction can be increased if deer and tick movement are controlled or even prohibited especially when there is an outbreak in one or both patches since movement can introduce a disease in an area that was initially disease-free. Thus, screening of infectives in protected areas such as deer farms, private game parks or reserves, etc. before they migrate to other areas can be one of the intervention strategies for controlling and preventing disease spread

Modelling Multiple Dosing with Drug Holiday in Antiretroviral Treatment on HIV-1 Infection

A within-host mathematical model to describe the dynamics of target cells and viral load in early HIV-1 infection was developed, which incorporates a combination of RTI and PI treatments by using a pharmacokinetics model. The local stability of uninfected steady state for the model was determined using an alternative threshold. The pharmacokinetics model was employed to estimate drug efficacy in multiple drug dosing. The effect of periodic drug efficacy of pharmacokinetic type on outcome of HIV-1 infection was explored under various treatment interruptions. The effectiveness of treatment interruption was determined according to the time period of the drug holidays. The results showed that long drug holidays lead to therapy failure. Under interruption of treatments combining RTI and PI therapy, effectiveness of the treatment requires a short duration of the drug holiday.

A mathematical model of contact tracing during the 2014-2016 west African ebola outbreak

The 2014-2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. Our aim in this work was to mechanistically represent the contact tracing process to illustrate potential areas of improvement in managing contact tracing efforts. We also explored the role contact tracing played in eventually ending the outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leonne during the outbreak. Using data on cumulative cases and deaths we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Our work highlights the importance of incorporatingchanging behavior into one’s model as needed when indicated by the data and reported trends. Our results show that a larger contact tracing program would have reduced the death toll of the outbreak. Counting the total number of people being traced and including changes in behavior in our model led to better understanding of disease management

Treatment of HIV-1 with Reverse Transcriptase Inhibitors ( RTI's) and Protease Inhibitors ( PI's )

Treatment with antiretroviral drugs has been reported to delay progression of HIV infection to AIDS, and may even lower the infectiousness of the infectives. This study investigates the effects of treatment of HIV-1 with Reverse Transcriptase Inhibitors (RTI's) and Protease Inhibitors (PI's) at cellular level. A threshold parameter, Ncrit, which determines the outcome of the infection, is established.If NT < Ncrit, the infection dies out, while if Ncrit < NT, the infection persists where NT is the number of virions produced by each infected CD4+_T cell. The steady states are determined for the models under study. Numerical simulations are presented to illustrate the stability of the endemic steady states

Modelling the Potential Impact of Stigma on the Transmission Dynamics of COVID-19 in South Africa

The COVID-19 pandemic continues to be a problem in South Africa. Individuals affected and infected by the disease suffer from stigma resulting in increased COVID-19 infections. In this paper, we developed a mathematical model to assess the effects of stigma on COVID-19 in South Africa, using low, moderate, and high stigma regimes in the population. The mathematical model was analysed and the basic reproduction number, R0, of the COVID-19 model with stigma was determined. The model was then fitted to data of the four COVID-19 waves for the new daily infected cases, and the estimated parameter values from different waves are presented. The effects of stigma on COVID-19 waves were examined using the four stigma regimes (high, moderate, low, and stigma-free regimes). Our results revealed that stigma is instrumental in the increase in the number of COVID-19 infections. It is also a significant contributor to sustaining COVID-19 in the population and probably in other infectious diseases such as HIV/AIDS and sexually transmitted diseases. The results obtained can influence policy directions with respect to stigma and its impact on the transmission dynamics of diseases

Understanding the transmission pathways of Lassa fever: A mathematical modeling approach

The spread of Lassa fever infection is increasing in West Africa over the last decade. The impact of this can better be understood when considering the various possible transmission routes. We designed a mathematical model for the epidemiology of Lassa Fever using a system of nonlinear ordinary differential equations to determine the effect of transmission pathways toward the infection progression in humans and rodents including those usually neglected such as the environmental surface and aerosol routes. We analyzed the model and carried out numerical simulations to determine the impact of each transmission routes. Our results showed that the burden of Lassa fever infection is increased when all the transmission routes are incorporated and most single transmission routes are less harmful, but when in combination with other transmission routes, they increase the Lassa fever burden. It is therefore important to consider multiple transmission routes to better estimate the Lassa fever burden optimally and in turn determine control strategies targeted at the transmission pathways

Table_1_Trans-Allelic Model for Prediction of Peptide:MHC-II Interactions.PDF

<p>Major histocompatibility complex class two (MHC-II) molecules are trans-membrane proteins and key components of the cellular immune system. Upon recognition of foreign peptides expressed on the MHC-II binding groove, CD4⁺ T cells mount an immune response against invading pathogens. Therefore, mechanistic identification and knowledge of physicochemical features that govern interactions between peptides and MHC-II molecules is useful for the design of effective epitope-based vaccines, as well as for understanding of immune responses. In this article, we present a comprehensive trans-allelic prediction model, a generalized version of our previous biophysical model, that can predict peptide interactions for all three human MHC-II loci (HLA-DR, HLA-DP, and HLA-DQ), using both peptide sequence data and structural information of MHC-II molecules. The advantage of this approach over other machine learning models is that it offers a simple and plausible physical explanation for peptide–MHC-II interactions. We train the model using a benchmark experimental dataset and measure its predictive performance using novel data. Despite its relative simplicity, we find that the model has comparable performance to the state-of-the-art method, the NetMHCIIpan method. Focusing on the physical basis of peptide–MHC binding, we find support for previous theoretical predictions about the contributions of certain binding pockets to the binding energy. In addition, we find that binding pocket P5 of HLA-DP, which was not previously considered as a primary anchor, does make strong contribution to the binding energy. Together, the results indicate that our model can serve as a useful complement to alternative approaches to predicting peptide–MHC interactions.</p