A mathematical model for malaria disease dynamics with vaccination and infected immigrants.

The world is aiming to eliminate malaria by 2030. The introduction of the pilot project on malaria vaccination for children in Kenya, Ghana, and Malawi presents a significant thrust to the elimination efforts. In this work, a susceptible, infectious and recovered (SIR) human-vector interaction mathematical model for malaria was formulated. The model was extended to include a compartment of vaccinated humans and an influx of infected immigrants. Qualitative and quantitative analysis was performed on the model. When there was no influx of infected immigrants, the model had a disease-free equilibrium point that was globally asymptotically stable when a threshold known as the basic reproductive number denoted by $ R_0 $ was less than one. When there was an influx of infected immigrants, the model had endemic equilibrium points only. Parameter sensitivity analysis on $ R_0 $ was performed and results showed that strategies must be implemented to reduce contact between mosquitoes and humans. Results from different vaccine coverage indicated that in the absence of an influx of infected immigrants, it is possible to achieve a malaria-free society when more children get vaccinated and the influx of infected humans is avoided. The analysis of the optimal control model showed that the combined use of vaccination, personal protective equipment, and treatment is the best way to curb malaria incidence, provided the influx of infected humans is completely stopped.

Projections of human papillomavirus vaccination and its impact on cervical cancer using the Caputo fractional derivative.

We propose a fractional order model for human papillomavirus (HPV) dynamics, including the effects of vaccination and public health education on developing cervical cancer. First, we discuss the general structure of Caputo fractional derivatives and integrals. Next, we define the fractional HPV model using Caputo derivatives. The model equilibrium quantities, with their stability, are discussed based on the magnitude of the reproduction number. We compute and simulate numerical solutions of the presented fractional model using the Adams-Bashforth-Moulton scheme. Meanwhile, real data sourced from reports from the World Health Organization is used to establish the parameters and compute the basic reproduction number. We present figures of state variables for different fractional orders and the classical integer order. The impacts of vaccination and public health education are discussed through numerical simulations. From the results, we observe that an increase in both vaccination rates and public health education increases the quality of life, and thus, reduces disease burden and suffering in communities. The results also confirm that modeling HPV transmission dynamics using fractional derivatives includes history effects in the model, making the model further insightful and appropriate for studying HPV dynamics.

Modeling the impact of combined use of COVID Alert SA app and vaccination to curb COVID-19 infections in South Africa.

The unanticipated continued deep-rooted trend of the Severe Acute Respiratory Syndrome Corona-virus-2 the originator pathogen of the COVID-19 persists posing concurrent anxiety globally. More effort is affixed in the scientific arena via continuous investigations in a prolific effort to understand the transmission dynamics and control measures in eradication of the epidemic. Both pharmaceutical and non-pharmaceutical containment measure protocols have been assimilated in this effort. In this study, we develop a modified SEIR deterministic model that factors in alternative-amalgamation of use of COVID Alert SA app and vaccination against the COVID-19 to the Republic of South Africa's general public in an endeavor to discontinue the chain of spread for the pandemic. We analyze the key properties of the model not limited to positivity, boundedness, and stability. We authenticate the model by fitting it to the Republic of South Africa's cumulative COVID-19 cases reported data utilizing the Maximum Likelihood Estimation algorithm implemented in fitR package. Sensitivity analysis and simulations for the model reveal that simultaneously-gradually increased implementation of the COVID Alert SA app use and vaccination against COVID-19 to the public substantially accelerate reduction in the plateau number of COVID-19 infections across all the observed vaccine efficacy scenarios. More fundamentally, it is discovered that implementing at least 12% app use (mainly for the susceptible population not vaccinated) with simultaneous vaccination of over 12% of the susceptible population majorly not using the app using a vaccine of at least 50% efficacy would be sufficient in eradicating the pandemic over relatively shorter time span.

Mathematical modeling and impact analysis of the use of COVID Alert SA app.

The human life-threatening novel Severe Acute Respiratory Syndrome Corona-virus-2 (SARS-CoV-2) has lasted for over a year escalating and posing simultaneous anxiety day-by-day globally since its first report in the late December 2019. The scientific arena has been kept animated via continuous investigations in an effort to understand the spread dynamics and the impact of various mitigation measures to keep this pandemic diminished. Despite a lot of research works having been accomplished this far, the pandemic is still deep-rooted in many regions worldwide signaling for more scientific investigations. This study joins the field by developing a modified SEIR (Susceptible-Exposed-Infectious-Removed) compartmental deterministic model whose key distinct feature is the incorporation of the COVID Alert SA app use by the general public in prolific intention to control the spread of the epidemic. Validation of the model is performed by fitting the model to the Republic of South Africa's COVID-19 cases reported data using the Maximum Likelihood Estimation algorithm implemented in fitR package. The model's sensitivity analysis and simulations stipulate that gradual to complete use of the app would be perfect in contact tracing and substantially reduce the plateau number of COVID-19 infections. This would consequentially contribute remarkably to the eradication of the SARS-CoV-2 over time. Proportional amalgamation of the app use and test for COVID-19 on individuals not using the app would also reduce the peak number of infections apart from the 50 - 50% ratio which spikes the plateau number beyond any other proportion. The study establishes that at least 30% implementation of the app use with gradual increase in tests conducted for individuals not using the app would suffice to stabilize the disease free equilibrium resulting to gradual eradication of the pandemic.

Assessing the role of human mobility on malaria transmission.

South Sudan accounts for a large proportion of all annual malaria cases in Africa. In recent years, the country has witnessed an unprecedented number of people on the move, refugees, internally displaced people, people who have returned to their counties or areas of origin, stateless people and other populations of concern, posing challenges to malaria control. Thus, one can claim that human mobility is one of the contributing factors to the resurgence of malaria. The aim of this paper is to assess the impact of human mobility on the burden of malaria disease in South Sudan. For this, we formulate an SIR-type model that describes the transmission dynamics of malaria disease between multiple patches. The proposed model is a system of stochastic differential equations consisting of ordinary differential equations perturbed by a stochastic Wiener process. For the deterministic part of the model, we calculate the basic reproduction number. Concerning the whole stochastic model, we use the maximum likelihood approach to fit the model to weekly malaria data of 2011 from Central Equatoria State, Western Bahr El Ghazal State and Warrap State. Using the parameters estimated on the fitted model, we simulate the future observation of the disease pattern. The disease was found to persist in the low transmission patches when there is human inflow in these patches and although the intervention coverage reaches 75%.

Assessing the role of climate factors on malaria transmission dynamics in South Sudan.

Malaria is endemic in South Sudan and it is one of the most severe diseases in the war-torn nation. There has been much concern about whether the severity of its transmission might depend upon climatic conditions that are related to the reproduction of the single-cell parasite attaching to female mosquitoes, especially in high altitude areas. The country experiences two different climatic conditions; namely one tropical and the other hot and semi-arid. In this study, we aim to assess the potential impact of climatic conditions on malaria prevalence in these two climatically distinct regions of South Sudan. We develop and analyze a host-mosquito disease-based model that includes temperature and rainfall. The model has also been parameterized in a Bayesian framework using Bayesian Markov Chain Monte Carlo (MCMC). The mathematical analysis for this study has included equilibria, stability and a sensitivity index on the basic reproduction number R0. The threshold R0 is also used to provide a numerical basis for further refinement and prediction of the impact of climate variability on malaria transmission intensity over the study region. The study highlights the impact of various temperature values on the population dynamics of the mosquito.

Modelling the effect of bednet coverage on malaria transmission in South Sudan.

A campaign for malaria control, using Long Lasting Insecticide Nets (LLINs) was launched in South Sudan in 2009. The success of such a campaign often depends upon adequate available resources and reliable surveillance data which help officials understand existing infections. An optimal allocation of resources for malaria control at a sub-national scale is therefore paramount to the success of efforts to reduce malaria prevalence. In this paper, we extend an existing SIR mathematical model to capture the effect of LLINs on malaria transmission. Available data on malaria is utilized to determine realistic parameter values of this model using a Bayesian approach via Markov Chain Monte Carlo (MCMC) methods. Then, we explore the parasite prevalence on a continued rollout of LLINs in three different settings in order to create a sub-national projection of malaria. Further, we calculate the model's basic reproductive number and study its sensitivity to LLINs' coverage and its efficacy. From the numerical simulation results, we notice a basic reproduction number, [Formula: see text], confirming a substantial increase of incidence cases if no form of intervention takes place in the community. This work indicates that an effective use of LLINs may reduce [Formula: see text] and hence malaria transmission. We hope that this study will provide a basis for recommending a scaling-up of the entry point of LLINs' distribution that targets households in areas at risk of malaria.