1st Mathematical Biology and Medicine Workshop (Virtual) | March 9-10, 2021

Affiliation - Department of Mathematics, Paa Grant University of Mines and Technology, Ghana 

A system of ordinary differential equations, is proposed to investigate the immune response to HBV infection. An optimal control representing drug treatment strategies for the proposed model is explored. Two types of treatments strategies are used. We investigate the qualitative behaviors of the model throughout the local stability of the steady states and bifurcation analysis. Existence and positivity of the solutions are investigated. Some interesting sufficient conditions that ensure the local asymptotic stability of infection-free and endemic steady states are studied. The proposed model and optimal control strategy adopted is shows how new viral production controlled. It is further shown

that new infection can be blocked to maintain the number of uninfected hepatocytes in a desirable range. The numerical solutions for control model is obtained to support our theoretical results.

Affiliation  - Department of Statistics, Kwame Nkrumah University of Science and Technology, Ghana

In this talk, I present to you the reliance of mathematical models and computations by most African countries towards the preparedness of COVID-19 amid our Vulnerabilities in Healthcare facilities. This talk is based on two papers that played a critical role among scientists on this continent dealing with this unchartered terrain of in-situ pandemic. These studies present how social distancing interventions such as school closure and prohibition of public gatherings are present in pandemic preparedness. Predicting the effectiveness of intervention strategies in a pandemic is difficult, hence in the absence of other evidence, computer simulation can be used to help policy makers plan for the pandemic.

The study conducted simulations of a small community to determine the magnitude and timing of activation that would be necessary for social distancing interventions to arrest the pandemic. Moreover, it is understood that, the management and control of COVID-19 importations heavily rely on a country’s health capacity. Here the study evaluate the preparedness and vulnerability of African countries against their risk of importation of COVID-19. The study used data on the volume of air travel departing from airports in the infected provinces in China and directed to Africa to estimate the risk of importation per country. The study determined the country’s capacity to detect and respond to cases with two indicators: preparedness, using the WHO International Health Regulations Monitoring and Evaluation Framework; and vulnerability, using the Infectious Disease Vulnerability Index. Countries were clustered according to the Chinese regions contributing most to their risk.

Affiliation - Department of Mathematics, University of Cape Coast, Ghana

A deterministic mathematical model for the transmission and control of malaria is formulated. The motivation for the model comes from the fact that, in a closed environment, an optimal combination of the percentage of people needed to carry out the preventative strategies (α) and the percentage of infected people needed to seek proper treatment can reduce both the number of infected human and infected mosquito populations, and eventually eliminate the disease from the community. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contribute to a reduction of the mosquito population. It was shown from the sensitivity analysis that the most sensitive parameter in the reduction of the basic reproduction number (R0) is α. Based on this result, numerical simulations were performed using different values of α to determine an optimal value of α that reduces the incidence rate fastest. It was observed that an optimal combination that reduces the incidence rate fastest comes from about 40% of adherence to the preventive strategies coupled with about 40% of infected humans seeking clinical treatment as this will reduces the infected human and vector populations considerably.

Affiliation -  Department of Biostatistics, University of Ghana 

The raging COVID-19 pandemic is arguably the most important threat to global health presently. Although there is currently a vaccine, preventive measures have been proposed to reduce the spread of infection but the efficacy of these interventions, and their likely impact on the number of COVID-19 infections is unknown. In this study, we proposed the SEIQHRS model (susceptible-exposed-infectious-quarantine-hospitalized-recovered-susceptible) model that predicts the trajectory of the epidemic to help plan an effective control strategy for COVID-19 in Ghana. We provided a short-term forecast of the early phase of the epidemic trajectory in Ghana using the generalized growth model. We estimated the effective basic Reproductive number Re in real-time using three different estimation procedures and simulated worse case epidemic scenarios and the impact of integrated individual and government interventions on the epidemic in the long term using compartmental models. The maximum likelihood estimates of Re and the corresponding 95%

confidence interval was 2.04 [95% CI: 1.82–2.27; 12th March-7th April 2020]. The Re estimate using the exponential growth method was 2.11 [95% CI: 2.00–2.24] within the same period. The Re estimate using time-dependent (TD) method showed a gradual decline of the Effective Reproductive Number since March 12, 2020 when the first 2 index cases were recorded but the rate of transmission remains high (TD: Re = 2.52; 95% CI: [1.87–3.49]). The current estimate of Re based on the TD method is 1.74 [95% CI: 1.41–2.10; (13th May 2020)] but with comprehensive integrated government and individual level interventions, the Re could reduce to 0.5 which is an indication of the epidemic dying out in the general population. Our results showed that enhanced government and individual-level interventions and the intensity of media coverage could have a substantial effect on suppressing transmission of new COVID-19 cases and reduced death rates in Ghana until such a time that a potent vaccine or drug is discovered.

Affiliation - Department of Mathematics, KNUST, Ghana

Coronavirus disease (COVID-19) is a novel infectious disease caused by the Severe Acute Respiratory Syndrome coronavirus 2 (SARS-CoV-2), resulting in a global pandemic. This paper uses COVID-19 data provided by the Ghana Health Service from the period 12 March 2020 to 31 May 2020 to: (1) estimate the basic reproduction number (R 0 ) using growth models, time-dependent daily and weekly reproduction number at the national level and other disease

parameters for COVID-19; (2) explain the epidemiology of the disease in Ghana taking into consideration the Ghanaian government’s imposition of non-pharmaceutical public health measures for mitigating the risk and impact of the pandemic; and (3) undertake morbidity and mortality analysis of COVID-19 cases. We utilise a modified Susceptible-Exposed-Infectious-Recovered (SEIR) compartmental model and other statistical models to achieve these

objectives. The initial reproduction number (R 0 ) is estimated as 3.205 using a 0.147 estimated growth rate and a 15-day time to recovery after COVID-19 infection while the estimated “effective” reproduction number (R eff ) of COVID-19 between March 12 and May 11, 2020 based on the mathematical compartmental SEIR model is 0.0772, indicating slow spread of the disease. We also find that the spread of the disease reduced consistently after the

imposition of the lockdown restrictions but increased following their removal. There is a need more robust mechanisms for tracing, testing, isolation and treatment. If the disease is to be brought under control (R 0 <1), then there is a need for (1) systematic testing of a representative sample of the population to monitor the reproduction number (2) increase in availability of testing for the general population to enable early detection, isolation and treatment of infected individuals to reduce progression to severe disease and mortality.

Affiliation : Department of Mathematics, University of Cape Coast, Ghana

In this talk, we present three (3) models based on SIR compartmental model. The basic SIR model is well-understood compartmental model, here, we will show how this basic model in combinations with isolation, quarantine, vaccination and treatment can help understand or to eliminate most infectious diseases if they are at the right time and in the right amount. We apply the optimal control theory to curtail the spread of infectious diseases by devising the optimal diseases intervention strategies usually consisting of minimizing the cost of infection or the cost of implementing the control, or both. This talk particularly serves as a good introduction to the Public health person or infectious diseases

expert who seeks to improve his knowledge.