Forecasting the spread of the COVID-19 pandemic in Kenya using SEIR and ARIMA models.

COVID-19, a coronavirus disease 2019, is an ongoing pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The first case in Kenya was identified on March 13, 2020, with the pandemic increasing to about 237,000 confirmed cases and 4,746 deaths by August 2021. We developed an SEIR model forecasting the COVID-19 pandemic in Kenya using an Autoregressive Integrated moving averages (ARIMA) model. The average time difference between the peaks of wave 1 to wave 4 was observed to be about 130 days. The 4th wave was observed to have had the least number of daily cases at the peak. According to the forecasts made for the next 60 days, the pandemic is expected to continue for a while. The 4th wave peaked on August 26, 2021 (498th day). By October 26, 2021 (60th day), the average number of daily infections will be 454 new cases and 40 severe cases, which would require hospitalization, and 16 critically ill cases requiring intensive care unit services. The findings of this study are key in developing informed mitigation strategies to ensure that the pandemic is contained and inform the preparedness of policymakers and health care workers.

Optimal control analysis of hepatocytic-erythrocytic dynamics of Plasmodium falciparum malaria.

This paper presents an in-host malaria model subject to anti-malarial drug treatment and malaria vaccine antigens combinations. Pontryagin's Maximum Principle is applied to establish optimal control strategies against infected erythrocytes, infected hepatocytes and malaria parasites. Results from numerical simulation reveal that a combination of pre-erythrocytic vaccine antigen, blood schizontocide and gametocytocide drugs would offer the best strategy to eradicate clinical P. falciparum malaria. Sensitivity analysis, further reveal that the efficacy of blood schizontocides and blood stage vaccines are crucial in the control of clinical malaria infection. Futhermore, we found that an effective blood schizontocide should be used alongside efficacious blood stage vaccine for rapid eradication of infective malaria parasites. The authors hope that the results of this study will help accelerate malaria elimination efforts by combining malaria vaccines and anti-malarial drugs against the deadly P. falciparum malaria.

SARS-COV-2 outbreak and control in Kenya - Mathematical model analysis.

The coronavirus disease 2019 (COVID-19) pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area Mombasa. As reported by the World Health Organization, the outbreak of COVID-19 has spread across the world, killed many, collapsed economies and changed the way people live since it was first reported in Wuhan, China, in the end of 2019. As at the end of December 2020, it had led to over 2.8 million confirmed cases in Africa with over 67 thousand deaths. The trend poses a huge threat to global public health. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. We employed a SEIHCRD mathematical transmission model with reported Kenyan data on cases of COVID-19 to estimate how transmission varies over time. The model is concise in structure, and successfully captures the course of the COVID-19 outbreak, and thus sheds light on understanding the trends of the outbreak. The next generation matrix approach was adopted to calculate the basic reproduction number (R 0) from the model to assess the factors driving the infection. The model illustrates the effect of mass testing on COVID-19 as well as individual self initiated behavioral change. The results have significant impact on the management of COVID-19 and implementation of prevention policies. The results from the model analysis shows that aggressive and effective mass testing as well as individual self initiated behaviour change play a big role in getting rid of the COVID-19 epidemic otherwise the rate of infection will continue to increase despite the increased rate of recovery.

SEIR model for COVID-19 dynamics incorporating the environment and social distancing.

OBJECTIVE: Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number [Formula: see text]. The model equations are solved numerically using fourth and fifth order Runge-Kutta methods. RESULTS: We found an [Formula: see text] of 2.03, implying that the pandemic will persist in the human population in the absence of strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus.

Multiple-Strain Malaria Infection and Its Impacts on Plasmodium falciparum Resistance to Antimalarial Therapy: A Mathematical Modelling Perspective.

The emergence of parasite resistance to antimalarial drugs has contributed significantly to global human mortality and morbidity due to malaria infection. The impacts of multiple-strain malarial parasite infection have further generated a lot of scientific interest. In this paper, we demonstrate, using the epidemiological model, the effects of parasite resistance and competition between the strains on the dynamics and control of Plasmodium falciparum malaria. The analysed model has a trivial equilibrium point which is locally asymptotically stable when the parasite's effective reproduction number is less than unity. Using contour plots, we observed that the efficacy of antimalarial drugs used, the rate of development of resistance, and the rate of infection by merozoites are the most important parameters in the multiple-strain P. falciparum infection and control model. Although the drug-resistant strain is shown to be less fit, the presence of both strains in the human host has a huge impact on the cost and success of antimalarial treatment. To reduce the emergence of resistant strains, it is vital that only effective antimalarial drugs are administered to patients in hospitals, especially in malaria-endemic regions. Our results emphasize the call for regular and strict surveillance on the use and distribution of antimalarial drugs in health facilities in malaria-endemic countries.

Modelling Optimal Control of In-Host HIV Dynamics Using Different Control Strategies.

HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles played by the various HIV treatment strategies. In particular, we establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables. We have applied Pontryagin's Maximum Principle in characterizing the optimality control, which then has been solved numerically by applying the Runge-Kutta forth-order scheme. The numerical results indicate that an optimal controlled treatment strategy would ensure significant reduction in viral load and also in HIV transmission. It is also evident from the results that protease inhibitor plays a key role in virus suppression; this is not to underscore the benefits accrued when all the three drug regimes are used in combination.

The In Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells.

The in vivo dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having R0 < 1. Lastly, the biological dynamics of HIV in vivo infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.