Analysis of War and Conflict Effect on the Transmission Dynamics of the Tenth Ebola Outbreak in the Democratic Republic of Congo.

The tenth Ebola outbreak in the Democratic Republic of Congo (DRC) that occurred from 2018 to 2020 was exacerbated by long-lasting conflicts and war in the region. We propose a deterministic model to investigate the impact of such disruptive events on the transmission dynamics of the Ebola virus disease. It is an extension of the classical susceptible-infectious-recovered model, enriched by an additional class of contaminated environment to account for indirect transmission as well as two classes of hospitalized individuals and patients who escape from the healthcare facility due to violence and attacks perpetrated by armed groups, rebels, etc. The model is formulated using two patches, namely Patch 1 consisting of the three affected eastern provinces in DRC and Patch 2, a war- and conflict-free area consisting of the go-to neighboring provinces for escaped patients. We introduce two key parameters, the escaping rate from hospitals and the destruction of hospitals, in terms of which the effect of war and conflicts is measured. The model is fitted and parameterized using the cumulative mortality data from the region. The basic reproduction number [Formula: see text] is computed and found to have a complex expression due to the high nonlinearity of the model. By using, not a Lyapunov function, but a decomposition theorem in Castillo-Chavez et al.(in Castillo-Chavez et al. (eds) Mathematical approaches for emerging and reemerging infectious diseases: an introduction, vol 126. Springer Science & Business Media, Berlin, 2002), it is shown that the disease-free equilibrium is globally asymptotically stable when [Formula: see text] and unstable when [Formula: see text]. A nonstandard finite difference scheme which replicates the dynamics of the continuous model is designed. In particular, a discrete counterpart of the above-mentioned theorem on the global asymptotic stability of the disease-free equilibrium is investigated. Numerical experiments are presented to support the theoretical results. When [Formula: see text], the numerical simulations suggest that there exists for the full model a unique globally asymptotically stable interior endemic equilibrium point, while it is shown theoretically and computationally that the model possesses at least a one Patch 1 and a one Patch 2 boundary equilibria (i.e., Patch 2 and Patch 1 disease-free equilibrium) points, which are locally asymptotically stable. Some recommendations to tackle Ebola in a conflict zone are stated.

Coupling the modeling of phage-bacteria interaction and cholera epidemiological model with and without optimal control.

In this work, we assess the impact of the phage-bacteria infection and optimal control on the indirectly transmitted cholera disease. The phage-bacteria interactions are described by predator-prey system using the Smith functional response, which takes into account the number of bacteria binding sites. The study is done in two steps, namely the model without control and the model with control. For the first scenario, we explicitly compute the basic reproduction number R0 which serves as stability threshold and bifurcation parameter. The proposed model exhibits a bi-stability phenomenon via the existence of backward bifurcation, which implies that the classical requirement of bringing the reproduction number under unity, while necessary, is no longer sufficient for cholera elimination from the population. We intuitively introduce a new threshold number N0 needed for the global stability of the disease free equilibrium point which is achieved when R0⩽1 and N0⩽1. It is further shown that the phage absorption is a possible cause of bi-stability, since in its absence, the condition R0⩽1 is sufficient for cholera to die out. The existence of endemic equilibrium points depends on the range of both R0 and N0. Regarding the model extended to an optimal control problem, which involves the use of virulent vibriophages to reduce or eliminate the bacteria population, we use optimal control theory techniques. We establish the conditions under which the spread of cholera can be stopped, and examine the impact of control measures on the transmission dynamic of cholera. The Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations suggest that, the release of lytic vibriophages can significantly reduce the spread of the disease. We discuss opportunities for phage therapy as treatment of some bacterial-borne diseases without side effects.

Mathematical modelling of the interactive dynamics of wild and Microsporidia MB-infected mosquitoes.

A recent discovery highlighted that mosquitoes infected with Microsporidia MB are unable to transmit the Plasmodium to humans. Microsporidia MB is a symbiont transmitted vertically and horizontally in the mosquito population, and these transmission routes are known to favor the persistence of the parasite in the mosquito population. Despite the dual transmission, data from field experiments reveal a low prevalence of MB-infected mosquitoes in nature. This study proposes a compartmental model to understand the prevalence of MB-infected mosquitoes. The dynamic of the model is obtained through the computation of the basic reproduction number and the analysis of the stability of the MB-free and coexistence equilibria. The model shows that, in spite of the high vertical transmission efficiency of Microsporidia MB, there can still be a low prevalence of MB-infected mosquitoes. Numerical analysis of the model shows that male-to-female horizontal transmission contributes more than female-to-male horizontal transmission to the spread of MB-infected mosquitoes. Moreover, the female-to-male horizontal transmission contributes to the spread of the symbiont only if there are multiple mating occurrences for male mosquitoes. Furthermore, when fixing the efficiencies of vertical transmission, the parameters having the greater influence on the ratio of MB-positive to wild mosquitoes are identified. In addition, by assuming a similar impact of the temperature on wild and MB-infected mosquitoes, our model shows the seasonal fluctuation of MB-infected mosquitoes. This study serves as a reference for further studies, on the release strategies of MB-infected mosquitoes, to avoid overestimating the MB-infection spread.

Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa.

Since its emergence late in 2019, the COVID-19 pandemic continues to exude major public health and socio-economic burden globally. South Africa is currently the epicenter for the pandemic in Africa. This study is based on the use of a compartmental model to analyze the transmission dynamics of the disease in South Africa. A notable feature of the model is the incorporation of the role of environmental contamination by COVID-infected individuals. The model, which is fitted and parametrized using cumulative mortality data from South Africa, is used to assess the impact of various control and mitigation strategies. Rigorous analysis of the model reveals that its associated continuum of disease-free equilibria is globally-asymptotically stable whenever the control reproduction number is less than unity. The epidemiological implication of this result is that the disease will eventually die out, particularly if control measures are implemented early and for a sustainable period of time. For instance, numerical simulations suggest that if the lockdown measures in South Africa were implemented a week later than the 26 March, 2020 date it was implemented, this will result in the extension of the predicted peak time of the pandemic, and causing about 10% more cumulative deaths. In addition to illustrating the effectiveness of self-isolation in reducing the number of cases, our study emphasizes the importance of surveillance testing and contact tracing of the contacts and confirmed cases in curtailing the pandemic in South Africa.

The Ross-Macdonald model in a patchy environment.

We generalize to n patches the Ross-Macdonald model which describes the dynamics of malaria. We incorporate in our model the fact that some patches can be vector free. We assume that the hosts can migrate between patches, but not the vectors. The susceptible and infectious individuals have the same dispersal rate. We compute the basic reproduction ratio R(0). We prove that if R(0)1, then the disease-free equilibrium is globally asymptotically stable. When R(0)>1, we prove that there exists a unique endemic equilibrium, which is globally asymptotically stable on the biological domain minus the disease-free equilibrium.

Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers.

In this paper, an epidemic model is investigated for infectious diseases that can be transmitted through both the infectious individuals and the asymptomatic carriers (i.e., infected individuals who are contagious but do not show any disease symptoms). We propose a dose-structured vaccination model with multiple transmission pathways. Based on the range of the explicitly computed basic reproduction number, we prove the global stability of the disease-free when this threshold number is less or equal to the unity. Moreover, whenever it is greater than one, the existence of the unique endemic equilibrium is shown and its global stability is established for the case where the changes of displaying the disease symptoms are independent of the vulnerable classes. Further, the model is shown to exhibit a transcritical bifurcation with the unit basic reproduction number being the bifurcation parameter. The impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission are discussed through through the local and the global sensitivity analyses of the basic reproduction number. Finally, a case study of hepatitis B virus disease (HBV) is considered, with the numerical simulations presented to support the analytical results. They further suggest that, in high HBV prevalence countries, the combination of effective vaccination (i.e. ≥ 3 doses of HepB vaccine), the diagnosis of asymptomatic carriers and the treatment of symptomatic carriers may have a much greater positive impact on the disease control.