A systematic review of mathematical models of Lassa fever.

This systematic review, conducted following the PRISMA guidelines, scrutinizes mathematical models employed in the study of Lassa fever. The analysis revealed the inherent heterogeneity in both models and data, posing significant challenges to parameter estimation. While health and behavioral interventions exhibit promise in mitigating the disease's spread, their efficacy is contingent upon contextual factors. Identified through this review are critical gaps, limitations, and avenues for future research, necessitating increased harmonization and standardization in modeling approaches. The considerations of seasonal and spatial variations emerge as crucial elements demanding targeted investigation. The perpetual threat of emerging diseases, coupled with the enduring public health impact of Lassa fever, underscores the imperative for sustained research endeavors and investments in mathematical modeling. The conclusion underscored that while mathematical modeling remains an invaluable tool in the combat against Lassa fever, its optimal utilization mandates multidisciplinary collaboration, refined data collection methodologies, and an enriched understanding of the intricate disease dynamics. This comprehensive approach is essential for effectively reducing the burden of Lassa fever and safeguarding the health of vulnerable populations.

Controlling malaria in a population accessing counterfeit antimalarial drugs.

A mathematical model is developed for describing malaria transmission in a population consisting of infants and adults and in which there are users of counterfeit antimalarial drugs. Three distinct control mechanisms, namely, effective malarial drugs for treatment and insecticide-treated bednets (ITNs) and indoor residual spraying (IRS) for prevention, are incorporated in the model which is then analyzed to gain an understanding of the disease dynamics in the population and to identify the optimal control strategy. We show that the basic reproduction number, $ R_{0} $, is a decreasing function of all three controls and that a locally asymptotically stable disease-free equilibrium exists when $ R_{0} < 1 $. Moreover, under certain circumstances, the model exhibits backward bifurcation. The results we establish support a multi-control strategy in which either a combination of ITNs, IRS and highly effective drugs or a combination of IRS and highly effective drugs is used as the optimal strategy for controlling and eliminating malaria. In addition, our analysis indicates that the control strategies primarily benefit the infant population and further reveals that a high use of counterfeit drugs and low recrudescence can compromise the optimal strategy.

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.

A vaccination model for COVID-19 in Gauteng, South Africa.

The COVID-19 pandemic provides an opportunity to explore the impact of government mandates on movement restrictions and non-pharmaceutical interventions on a novel infection, and we investigate these strategies in early-stage outbreak dynamics. The rate of disease spread in South Africa varied over time as individuals changed behavior in response to the ongoing pandemic and to changing government policies. Using a system of ordinary differential equations, we model the outbreak in the province of Gauteng, assuming that several parameters vary over time. Analyzing data from the time period before vaccination gives the approximate dates of parameter changes, and those dates are linked to government policies. Unknown parameters are then estimated from available case data and used to assess the impact of each policy. Looking forward in time, possible scenarios give projections involving the implementation of two different vaccines at varying times. Our results quantify the impact of different government policies and demonstrate how vaccinations can alter infection spread.

Modeling the Effect of HIV/AIDS Stigma on HIV Infection Dynamics in Kenya.

Stigma toward people living with HIV/AIDS (PLWHA) has impeded the response to the disease across the world. Widespread stigma leads to poor adherence of preventative measures while also causing PLWHA to avoid testing and care, delaying important treatment. Stigma is clearly a hugely complex construct. However, it can be broken down into components which include internalized stigma (how people with the trait feel about themselves) and enacted stigma (how a community reacts to an individual with the trait). Levels of HIV/AIDS-related stigma are particularly high in sub-Saharan Africa, which contributed to a surge in cases in Kenya during the late twentieth century. Since the early twenty-first century, the United Nations and governments around the world have worked to eliminate stigma from society and resulting public health education campaigns have improved the perception of PLWHA over time, but HIV/AIDS remains a significant problem, particularly in Kenya. We take a data-driven approach to create a time-dependent stigma function that captures both the level of internalized and enacted stigma in the population. We embed this within a compartmental model for HIV dynamics. Since 2000, the population in Kenya has been growing almost exponentially and so we rescale our model system to create a coupled system for HIV prevalence and fraction of individuals that are infected that seek treatment. This allows us to estimate model parameters from published data. We use the model to explore a range of scenarios in which either internalized or enacted stigma levels vary from those predicted by the data. This analysis allows us to understand the potential impact of different public health interventions on key HIV metrics such as prevalence and disease-related death and to see how close Kenya will get to achieving UN goals for these HIV and stigma metrics by 2030.

Evidence-based modeling of combination control on Kenyan youth HIV/AIDS dynamics.

We formulate a sex-structured deterministic model to study the effects of varying HIV testing rates, condom use rates and ART adherence rates among Adolescent Girls and Young Women (AGYW) and, Adolescent Boys and Young Men (ABYM) populations in Kenya. Attitudes influencing the Kenyan youth HIV/AIDS control measures both positively and negatively were considered. Using the 2012 Kenya AIDS Indicator Survey (KAIS) microdata we constructed our model, which we fitted to the UNAIDS-Kenya youth prevalence estimates to understand factors influencing Kenyan youth HIV/AIDS prevalence trends. While highly efficacious combination control approach significantly reduces HIV/AIDS prevalence rates among the youth, the disease remains endemic provided infected unaware sexual interactions persist. Disproportional gender-wise attitudes towards HIV/AIDS control measures play a key role in reducing the Kenyan youth HIV/AIDS prevalence trends. The female youth HIV/AIDS prevalence trend seems to be directly linked to increased male infectivity with decreased female infectivity while the male youth prevalence trend seems to be directly associated with increased female infectivity and reduced male infectivity.

A general method for multiscale modelling of vector-borne disease systems.

The inability to develop multiscale models which can describe vector-borne disease systems in terms of the complete pathogen life cycle which represents multiple targets for control has hindered progress in our efforts to control, eliminate and even eradicate these multi-host infections. This is because it is currently not easy to determine precisely where and how in the life cycles of vector-borne disease systems the key constrains which are regarded as crucial in regulating pathogen population dynamics in both the vertebrate host and vector host operate. In this article, we present a general method for development of multiscale models of vector-borne disease systems which integrate the within-host and between-host scales for the two hosts (a vertebrate host and a vector host) that are implicated in vector-borne disease dynamics. The general multiscale modelling method is an extension of our previous work on multiscale models of infectious disease systems which established a basic science and accompanying theory of how pathogen population dynamics at within-host scale scales up to between-host scale and in turn how it scales down from between-host scale to within-host scale. Further, the general method is applied to multiscale modelling of human onchocerciasis-a vector-borne disease system which is sometimes called river blindness as a case study.

Acute hepatitis B virus infection model within the host incorporating immune cells and cytokine responses.

We formulate and analyze a within-host hepatitis B viral mathematical model for hepatitis B in the acute phase of infection. The model incorporates hepatocytes, hepatitis B virus, immune system cells and cytokine dynamics using a system of ordinary differential equations. We use the model to demonstrate the trends of the hepatitis B infection qualitatively without the effects of immune cells and cytokines. Using these trends, we tested the effects of incorporating the immune cells only and immune cells with cytokine responses at low and high inhibitions on the hepatitis B virus infection. Our results showed that it is impossible to have the immune cells work independently from cytokines when there is an acute hepatitis B virus infection. Therefore, our results suggest that incorporating immune cells and cytokine dynamics in the acute hepatitis B virus infection stage delays infection in the hepatocytes and excluding such dynamics speeds up infection during this phase. Results from this study are useful in developing strategies for control of hepatocellular carcinoma which is caused by hepatitis B virus infection.

Predicting Antigenicity of Influenza A Viruses Using biophysical ideas.

Antigenic variations of influenza A viruses are induced by genomic mutation in their trans-membrane protein HA1, eliciting viral escape from neutralization by antibodies generated in prior infections or vaccinations. Prediction of antigenic relationships among influenza viruses is useful for designing (or updating the existing) influenza vaccines, provides important insights into the evolutionary mechanisms underpinning viral antigenic variations, and helps to understand viral epidemiology. In this study, we present a simple and physically interpretable model that can predict antigenic relationships among influenza A viruses, based on biophysical ideas, using both genomic amino acid sequences and experimental antigenic data. We demonstrate the applicability of the model using a benchmark dataset of four subtypes of influenza A (H1N1, H3N2, H5N1, and H9N2) viruses and report on its performance profiles. Additionally, analysis of the model's parameters confirms several observations that are consistent with the findings of other previous studies, for which we provide plausible explanations.

A stochastic epidemic model for the dynamics of two pathogens in a single tick population.

Understanding tick-transmitted pathogens in tick infested areas is crucial for the development of preventive and control measures in response to the increasing cases of tick-borne diseases. A stochastic model for the dynamics of two pathogens, Rickettsia parkeri and Rickettsia amblyommii, in a single tick, Amblyomma americanum, is developed and analysed. The model, a continuous-time Markov chain, is based on a deterministic tick-borne disease model. The extinction threshold for the stochastic model is computed using the multitype branching process and conditions for pathogen extinction or persistence are presented. The probability of pathogen extinction is computed using numerical simulations and is shown to be a good estimate of the probability of extinction calculated from the branching process. A sensitivity analysis is undertaken to illustrate the relationship between co-feeding and transovarial transmission rates and the probability of pathogen extinction. Expected epidemic duration is estimated using sample paths and we show that R. amblyommii is likely to persist slightly longer than R. parkeri. Further, we estimate the duration of possible coexistence of the two pathogens.

Modeling the effects of insecticides resistance on malaria vector control in endemic regions of Kenya.

We present a model to investigate the effects of vector resistance to control strategies. The model captures the development of resistance as well as loss of resistance in mosquitoes and how these affect the progress in malaria control. Important thresholds were calculated from mathematical analysis and numerical results presented. Mathematical results reveal the existence of the disease free and endemic equilibria whose existence and stability depends on the control reproduction number, Rc. The disease persist when the Rc>1 and dies out when Rc<1. Control strategies use and adherence needs to be highly efficacious to thwart the effects of insecticides resistance. Moreover, it is not enough to just eradicate resistant mosquitoes.

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

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.

Modelling coupled within host and population dynamics of [Formula: see text] and [Formula: see text] HIV infection.

Most existing models have considered the immunological processes occurring within the host and the epidemiological processes occurring at population level as decoupled systems. We present a new model using continuous systems of non linear ordinary differential equations by directly linking the within host dynamics capturing the interactions between Langerhans cells, CD4[Formula: see text] T-cells, R5 HIV and X4 HIV and the without host dynamics of a basic compartmental HIV/AIDS model. The model captures the biological theories of the cells that take part in HIV transmission. The study incorporates in its analysis the differences in time scales of the fast within host dynamics and the slow without host dynamics. In the mathematical analysis, important thresholds, the reproduction numbers, were computed which are useful in predicting the progression of the infection both within the host and without the host. The study results showed that the model exhibits four within host equilibrium points inclusive of three endemic equilibria whose effects translate into different scenarios at the population level. All the endemic equilibria were shown to be globally stable using Lyapunov functions and this is an important result in linking the within host dynamics to the population dynamics, because the disease free equilibrium point ceases to exist. The effects of linking were observed on the endemic equilibrium points of both the within host and population dynamics. Linking the two dynamics was shown to increase in the viral load within the host and increase in the epidemic levels in the population dynamics.

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence.

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

Pre-exposure prophylaxis and antiretroviral treatment interventions with drug resistance.

We introduce a model for HIV/AIDS which can be utilized to assess the impact of combining pre-exposure prophylaxis (PrEP) and antiretroviral drugs (ARVs) use interventions (incorporating drug resistance). Mathematical and numerical analyses are carried out to investigate the effects of the combined controls in the presence of PrEP drug resistance. Our results predict a significant decrease in the number of new HIV infections when PrEP and ARVs are concurrently implemented at high levels. The results also reveal that PrEP drug resistance has the potential to slow down or reverse the effects of PrEP, especially at low efficacy levels.

Modelling the role of multi-transmission routes in the epidemiology of bovine tuberculosis in cattle and buffalo populations.

A mathematical model that describes the transmission dynamics of bovine tuberculosis (BTB) in both buffalo and cattle populations is proposed. The model incorporates cross-infection and contaminated environment transmission routes. A full analysis of the model is undertaken. The reproduction number of the entire model is comprised of cross-infection and contaminated parameters. This underscores the importance of including both cross-infection and contaminated environment transmission routes. Crucially our simulations suggest that the disease has a more devastating effect on cattle populations than on buffalo populations when all transmission routes are involved. This has important implications for agriculture and tourism.

Effects of replicative fitness on competing HIV strains.

We develop an n-strain model to show the effects of replicative fitness of competing viral strains exerting selective density-dependant infective pressure on each other. A two strain model is used to illustrate the results. A perturbation technique and numerical simulations were used to establish the existence and stability of steady states. More than one infected steady states governed by the replicative fitness resulted from the model exhibiting either strain replacement or co-infection. We found that the presence of two or more HIV strains could result in a disease-free state that, in general, is not globally stable.