Mathematical modeling of infectious and non communicable diseases: exploring public health intervention strategies

As new viruses and new pandemics emerge we face the question as to whether

our global health systems are well prepared to deal with them. Non pharma ceutical measures are a key control measure in the battle against infectious

diseases especially in the absence of vaccines or when available vaccine

quantities are not sufficient. 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 presented a system of ordinary differential

equations to model contact tracing in Sierra Leonne during the outbreak.

We included 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 highlighted the importance of incorporating changing behavior into one’s

model as needed when indicated by the data and reported trends. Our results

showed 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.

Viral outbreaks differ in many ways, despite these differences policy responses

used to tackle viral epidemics tend to be similar across time and countries.

Substantial progress has been made since the 2014-2016 Ebola outbreak with

lessons learnt from previous and ongoing outbreaks followed by significant

investments into surveillance and preparedness and this has been of help in

dealing with the COVID-19 pandemic. We formulated a mathematical model

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for the spread of the coronavirus which incorporated adherence to disease

prevention. The major results of this study were: first, we determined optimal

infection coefficients such that high levels of coronavirus transmission were

prevented. Secondly, we found that there existed several optimal pairs of

removal rates, from the general population of asymptomatic and symptomatic

infectives respectively that could protect hospital bed capacity and flatten

the hospital admission curve. Of the many optimal strategies, this study

recommended the pair that yielded the least number of coronavirus related

deaths. The results for South Africa, which is better placed than the other

sub-Sahara African countries, showed that failure to address hygiene and

adherence issues will preclude the existence of an optimal strategy and could

result in a more severe epidemic than the Italian COVID-19 epidemic. Relaxing

lockdown measures to allow individuals to attend to vital needs such as food

replenishment increases household and community infection rates and the

severity of the overall infection.

Although the tobacco epidemic is one of the biggest health threats, responsible

for more than 8 million deaths annually with 15% of these caused by second

hand smoke , only a few mathematical models have addressed smoking in the

context of lung cancer. In our work we present two models, a stochastic model

and a deterministic model both of which are fitted to actual smoking data. The

expected solution of the stochastic model predicts a steady state solution in the

long run for the moderate and heavy smokers with proportions of these popu lations remaining to sustain the habit contrary to the trend in the actual data

which suggests extinction of these populations. The deterministic model, re vealed that the presence of highly quantifiable efficacious control measures can

reduce the lung cancer load by 50% although the number of lung cancer deaths

would remain the same for sometime. These results confirm the conclusions

of the stochastic model and reveal further that these control measures can re duce the lung cancer load and lung cancer deaths by about 50% if there is a

reduction of at least 20% in the population of susceptible individuals taking up

smoking. Specifically, if the number of new potential (susceptible) smokers ex xiv

ceeds a quantifiable threshold, Λ then even if R0 < 1 there is persistence of

the epidemic.