Mathematical Modelling and Analysis of Transmission Dynamics of Lassa Fever

Abstract

Sub-Saharan Africa harbours the majority of the burden of Lassa fever. Clinical diseases, as well as high seroprevalence, has been documented in Nigeria, Sierra Leone, Liberia, Guinea, Ivory Coast, Ghana, Senegal, Upper Volta, Gambia, and Mali. Deaths from Lassa fever occur all year round but naturally peak during the dry season. Annually, the number of people infected is estimated at 100,000 to 300,000, with approximately 5,000 deaths. There have been some few works done on the dynamics of Lassa fever disease transmission but to the best of our knowledge none has been able to capture the seasonal variation of mastomys rodents population and its impact on the transmission dynamics. In this work, a periodically-forced seasonal non-autonomous system of a non-linear ordinary differential equation is developed that captures the dynamics of Lassa fever transmission and seasonal variation in the birth of mastomys rodents where time was measured in days to capture seasonality. It was shown that the model is epidemiologically meaningful and mathematically well-posed by using the results from the qualitative properties of the solution of the model. A time-dependent basic reproduction number RL(t), is obtained such that its yearly average is written as RL < 1, when the disease does not invade the population (means that the number of infected humans always decrease in the following seasons of transmission) and RL > 1 when the disease remains constantly and is invading the population and it was detected that RL = RL. We also performed some evaluation of the Lassa fever disease intervention strategies using the elasticity of the equilibrial prevalence in order to predict the optimal intervention strategies that can be useful in guiding the local national control program on Lassa fever disease to make a proper decision on the intervention packages. Numerical simulations were carried out to illustrate the analytical results and we found that the numerical simulations of the model showed that possible combined intervention strategies would reduce the spread of the disease. It was established that, to eliminate Lassa fever disease, treatments with Ribavirin must be provided early to reduce mortality and other preventive measures like an educational campaign, community hygiene, Isolation of infected humans, and culling/destruction of rodents must be applied to also reduce the morbidity of the disease. Finally, the obtained results gave a primer framework for planning and designing cost-effective strategies for good interventions in eliminating Lassa fever.

An optimal control model for the transmission dynamics of Lassa fever

“…Several mathematical models have been developed to understand the dynamics of Lassa fever within a population. Ibrahim et al [3] and Bakare et al [4] presented a periodic model for Lassa fever transmission dynamics. Their results suggest interventions should be employed for the elimination of the Lassa virus within the community.…”

“…However, their models did not include optimal control analysis of intervention measures [3]. Bakare et al [4] further pointed out that a combination of intervention measures such as treatment of Lassa fever with Ribavirin, educating the community on how to practice environmental hygiene, isolation of infected Lassa fever patients and the probable culling any rodents found, could marginally reduce the prevalence of Lassa fever and its mortality rate [4]. Okolo et al [5] developed a model for the dynamics of Lassa fever in the presence of isolation and treatment.…”

Dynamical System Analysis of a Lassa Fever Model with Varying Socioeconomic Classes

“…A number of mathematical models such as [7][8][9][10][11][12][13][14] have explored the dynamics of Lassa fever. Lassa fever has been at the center of infectious disease.…”

Modeling the dynamics of Lassa fever in Nigeria

“…Bakare's research [6] developed a non-autonomous system of nonlinear ordinary differential equations that capture the dynamics of LF transmission and seasonal variation in Mastomys rodent birth. The authors of the study evaluate LF disease intervention strategies by predicting optimal intervention best fit in controlling the disease in the population using the elasticity of the equilibria prevalence.…”